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 A001248 Squares of primes. 590
 4, 9, 25, 49, 121, 169, 289, 361, 529, 841, 961, 1369, 1681, 1849, 2209, 2809, 3481, 3721, 4489, 5041, 5329, 6241, 6889, 7921, 9409, 10201, 10609, 11449, 11881, 12769, 16129, 17161, 18769, 19321, 22201, 22801, 24649, 26569, 27889, 29929, 32041, 32761, 36481 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Also 4, together with numbers n such that Sum_{d|n}(-1)^d = -A048272(n) = -3. - Benoit Cloitre, Apr 14 2002 Also, all solutions to the equation sigma(x) + phi(x) = 2x + 1. - Farideh Firoozbakht, Feb 02 2005 Unique numbers having 3 divisors (1, their square root, themselves). - Alexandre Wajnberg, Jan 15 2006 Smallest (or first) new number deleted at the n-th step in an Eratosthenes sieve. - Lekraj Beedassy, Aug 17 2006 Subsequence of semiprimes A001358. - Lekraj Beedassy, Sep 06 2006 Integers having only 1 factor other than 1 and the number itself. Every number in the sequence is a multiple of 1 factor other than 1 and the number itself. 4 : 2 is the only factor other than 1 and 4; 9 : 3 is the only factor other than 1 and 9; and so on. - Rachit Agrawal (rachit_agrawal(AT)daiict.ac.in), Oct 23 2007 The n-th number with p divisors is equal to the n-th prime raised to power p-1, where p is prime. - Omar E. Pol, May 06 2008 There are 2 Abelian groups of order p^2 (C_p^2 and C_p x C_p) and no non-Abelian group. - Franz Vrabec, Sep 11 2008 Also numbers n such that phi(n) = n - sqrt(n). - Michel Lagneau, May 25 2012 For n > 1, n is the sum of numbers from A006254(n-1) to A168565(n-1). - Vicente Izquierdo Gomez, Dec 01 2012 A078898(a(n)) = 2. - Reinhard Zumkeller, Apr 06 2015 Let r(n) = (a(n) - 1)/(a(n) + 1); then Product_{n>=1} r(n) = (3/5) * (4/5) * (12/13) * (24/25) * (60/61) * ... = 2/5. - Dimitris Valianatos, Feb 26 2019 Numbers k such that A051709(k) = 1. - Jianing Song, Jun 27 2021 LINKS Ray Chandler, Table of n, a(n) for n = 1..10000 (first 5000 terms from N. J. A. Sloane) R. P. Boas and N. J. A. Sloane, Correspondence, 1974 Marius Coman, On the special relation between the numbers of the form 505+ 1008k and the squares of primes, 2015. Brady Haran and Matt Parker, Squaring Primes, Numberphile video (2018). Eric Weisstein's World of Mathematics, Prime Power. OEIS Wiki, Index entries for number of divisors Index to sequences related to prime signature FORMULA n such that A062799(n) = 2. - Benoit Cloitre, Apr 06 2002 A000005(a(n)^(k-1)) = A005408(k) for all k>0. - Reinhard Zumkeller, Mar 04 2007 a(n) = A000040(n)^(3-1)=A000040(n)^2, where 3 is the number of divisors of a(n). - Omar E. Pol, May 06 2008 A000005(a(n)) = 3 or A002033(a(n)) = 2. - Juri-Stepan Gerasimov, Oct 10 2009 A033273(a(n)) = 3. - Juri-Stepan Gerasimov, Dec 07 2009 For n > 2: (a(n) + 17) mod 12 = 6. - Reinhard Zumkeller, May 12 2010 A192134(A095874(a(n))) = A005722(n) + 1. - Reinhard Zumkeller, Jun 26 2011 For n > 2: a(n) = 1 (mod 24). - Zak Seidov, Dec 07 2011 A211110(a(n)) = 2. - Reinhard Zumkeller, Apr 02 2012 a(n) = A087112(n,n). - Reinhard Zumkeller, Nov 25 2012 a(n) = prime(n)^2. - Jon E. Schoenfield, Mar 29 2015 Product_{n>=1} a(n)/(a(n)-1) = Pi^2/6. - Daniel Suteu, Feb 06 2017 Sum_{n>=1} 1/a(n) = P(2) = 0.4522474200... (A085548). - Amiram Eldar, Jul 27 2020 From Amiram Eldar, Jan 23 2021: (Start) Product_{n>=1} (1 + 1/a(n)) = zeta(2)/zeta(4) = 15/Pi^2 (A082020). Product_{n>=1} (1 - 1/a(n)) = 1/zeta(2) = 6/Pi^2 (A059956). (End) MAPLE A001248:=n->ithprime(n)^2; seq(A001248(k), k=1..50); # Wesley Ivan Hurt, Oct 11 2013 MATHEMATICA Prime[Range[30]]^2 (* Zak Seidov, Dec 07 2011 *) Select[Range[40000], DivisorSigma[0, #] == 3 &] (* Carlos Eduardo Olivieri, Jun 01 2015 *) PROG (PARI) forprime(p=2, 1e3, print1(p^2", ")) \\ Charles R Greathouse IV, Jun 10 2011 (PARI) A001248(n)=prime(n)^2 \\ M. F. Hasler, Sep 16 2012 (Haskell) a001248 n = a001248_list !! (n-1) a001248_list = map (^ 2) a000040_list -- Reinhard Zumkeller, Sep 23 2011 (Magma) [p^2: p in PrimesUpTo(300)]; // Vincenzo Librandi, Mar 27 2014 (SageMath) [n^2 for n in prime_range(1, 301)] # G. C. Greubel, May 02 2024 CROSSREFS Cf. A000005, A000040, A001358, A001694, A002033, A005408, A005722, A006254. Cf. A008864, A033273, A049001, A048272, A051709, A059956, A060800, A062799. Cf. A078898, A082020, A085548, A087112, A095874, A168565, A192134, A211110. Cf. A258599. Subsequence of A000430, A001358, and of A190641. Cf. A024450 (partial sums), A069482 (first differences). Sequence in context: A247078 A077438 A350343 * A280076 A359757 A052043 Adjacent sequences: A001245 A001246 A001247 * A001249 A001250 A001251 KEYWORD nonn,easy AUTHOR N. J. A. Sloane STATUS approved

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Last modified June 24 12:27 EDT 2024. Contains 373677 sequences. (Running on oeis4.)