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A001248
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Squares of primes.
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176
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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
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OFFSET
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1,1
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COMMENTS
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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
A000005(a(n)^(k-1)) = A005408(k) for all k>0. - Reinhard Zumkeller, Mar 04 2007
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. [From Franz Vrabec, Sep 11 2008]
For n > 2: (a(n) + 17) mod 12 = 6. [From 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). - Moshe Levin, Dec 07 2011
A211110(a(n)) = 2. [Reinhard Zumkeller, Apr 02 2012]
Solutions of the differential equation n'=2*sqrt(n), where n' is the arithmetic derivative of n. [Paolo P. Lava, Apr 23 2012]
Also numbers n such that phi(n) = n - sqrt(n). - Michel Lagneau, May 25 2012
a(n) = A087112(n,n). - Reinhard Zumkeller, Nov 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
Numbers whose multiplicative projection (A000026) is equal to their arithmetic derivative (A003415). [Paolo P. Lava, Dec 11 2012]
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LINKS
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N. J. A. Sloane, Table of n, a(n) for n = 1..5000
Eric Weisstein's World of Mathematics, Prime Power
OEIS Wiki, Index entries for number of divisors
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FORMULA
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n such that A062799(n)=2 - Benoit Cloitre, Apr 06 2002
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. [From Juri-Stepan Gerasimov, Dec 07 2009]
a(n) = 1 + 24*A024702(n), n >= 3. - Omar E. Pol, Dec 07 2011
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MATHEMATICA
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Prime[Range[30]]^2 (* Moshe Levin, Dec 07 2011 *)
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PROG
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(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
(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
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CROSSREFS
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Cf. A000040, A049001, A024450, A008864, A060800.
Subsequence of A000430.
Sequence in context: A068999 A179707 A077438 * A052043 A188836 A030146
Adjacent sequences: A001245 A001246 A001247 * A001249 A001250 A001251
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KEYWORD
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nonn,easy,changed
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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