|
%I
%S 4,9,25,49,121,169,289,361,529,841,961,1369,1681,1849,2209,2809,3481,
%T 3721,4489,5041,5329,6241,6889,7921,9409,10201,10609,11449,11881,
%U 12769,16129,17161,18769,19321,22201,22801,24649,26569,27889,29929,32041,32761,36481
%N Squares of primes.
%C Also 4, together with numbers n such that sum(d|n,(-1)^d) = -A048272(n) = -3 - _Benoit Cloitre_, Apr 14 2002
%C Also, all solutions to the equation sigma(x)+phi(x)=2x+1. - Farideh Firoozbakht, Feb 02 2005
%C Unique numbers having 3 divisors (1, their square root, themselves). - _Alexandre Wajnberg_, Jan 15 2006
%C Smallest (or first) new number deleted at the n-th step in an Eratosthenes sieve. - _Lekraj Beedassy_, Aug 17 2006
%C Subsequence of semiprimes A001358. - _Lekraj Beedassy_, Sep 06 2006
%C A000005(a(n)^(k-1)) = A005408(k) for all k>0. - _Reinhard Zumkeller_, Mar 04 2007
%C 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
%C 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
%C There are 2 Abelian groups of order p^2 (C_p^2 and C_p x C_p) and no non-Abelian group. [From _Franz Vrabec_, Sep 11 2008]
%C For n > 2: (a(n) + 17) mod 12 = 6. [From _Reinhard Zumkeller_, May 12 2010]
%C A192134(A095874(a(n))) = A005722(n) + 1. [_Reinhard Zumkeller_, Jun 26 2011]
%C For n > 2: a(n) = 1 (mod 24). - Moshe Levin, Dec 07 2011
%C A211110(a(n)) = 2. [_Reinhard Zumkeller_, Apr 02 2012]
%C Solutions of the differential equation n'=2*sqrt(n), where n' is the arithmetic derivative of n. [_Paolo P. Lava_, Apr 23 2012]
%C Also numbers n such that phi(n) = n - sqrt(n). - Michel Lagneau, May 25 2012
%C a(n) = A087112(n,n). - _Reinhard Zumkeller_, Nov 25 2012
%C For n > 1, n is the sum of numbers from A006254(n-1) to A168565(n-1). - _Vicente Izquierdo Gomez_, Dec 01 2012
%C Numbers whose multiplicative projection (A000026) is equal to their arithmetic derivative (A003415). [_Paolo P. Lava_, Dec 11 2012]
%H N. J. A. Sloane, <a href="/A001248/b001248.txt">Table of n, a(n) for n = 1..5000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimePower.html">Prime Power</a>
%H OEIS Wiki, <a href="https://oeis.org/wiki/Index_entries_for_number_of_divisors">Index entries for number of divisors</a>
%F n such that A062799(n)=2 - _Benoit Cloitre_, Apr 06 2002
%F 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
%F A000005(a(n))=3 or A002033(a(n))=2. - _Juri-Stepan Gerasimov_, Oct 10 2009
%F A033273(a(n))=3. [From _Juri-Stepan Gerasimov_, Dec 07 2009]
%F a(n) = 1 + 24*A024702(n), n >= 3. - Omar E. Pol, Dec 07 2011
%t Prime[Range[30]]^2 (* Moshe Levin, Dec 07 2011 *)
%o (SAGE) BB = primes_first_n(36) list = [] for i in range(36): list.append(BB[i]^2) list - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 15 2007
%o (PARI) forprime(p=2,1e3,print1(p^2", ")) \\ _Charles R Greathouse IV_, Jun 10 2011
%o (PARI) A001248(n)=prime(n)^2 \\ - _M. F. Hasler_, Sep 16 2012
%o (Haskell)
%o a001248 n = a001248_list !! (n-1)
%o a001248_list = map (^ 2) a000040_list -- _Reinhard Zumkeller_, Sep 23 2011
%Y Cf. A000040, A049001, A024450, A008864, A060800.
%Y Subsequence of A000430.
%K nonn,easy,changed
%O 1,1
%A _N. J. A. Sloane_.
| 