Search: id:A001248
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%I A001248
%S A001248 4,9,25,49,121,169,289,361,529,841,961,1369,1681,1849,2209,
%T A001248 2809,3481,3721,4489,5041,5329,6241,6889,7921,9409,10201,
%U A001248 10609,11449,11881,12769,16129,17161,18769,19321,22201
%N A001248 Squares of primes.
%C A001248 Also 4, together with numbers n such that sum(d|n,(-1)^d) = -A048272(n) 
               = -3 - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 14 2002
%C A001248 Also, all solutions to the equation sigma(x)+phi(x)=2x+1. - Farideh Firoozbakht, 
               Feb 02 2005
%C A001248 Unique numbers having 3 divisors (1, their square root, themselves). 
               - Alexandre Wajnberg (alexandre.wajnberg(AT)skynet.be), Jan 15 2006
%C A001248 Smallest (or first) new number deleted at the n-th step in an Eratosthenes 
               sieve. - Lekraj Beedassy (blekraj(AT)yahoo.com), Aug 17 2006
%C A001248 Subsequence of semiprimes A001358. - Lekraj Beedassy (blekraj(AT)yahoo.com), 
               Sep 06 2006
%C A001248 A000005(a(n)^(k-1)) = A005408(k) for all k>0. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Mar 04 2007
%C A001248 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 A001248 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 (info(AT)polprimos.com), 
               May 06 2008
%C A001248 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 (franz.vrabec(AT)aon.at), Sep 
               11 2008]
%C A001248 Free divisors of n or two perfect partitions of n. [From Juri-Stepan 
               Gerasimov (2stepan(AT)rambler.ru), Nov 19 2009]
%H A001248 N. J. A. Sloane, <a href="b001248.txt">Table of n, a(n) for n = 1..5000</
               a>
%H A001248 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PrimePower.html">Link to a section of The World of Mathematics.</
               a>
%F A001248 n such that A062799(n)=2 - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Apr 06 2002
%F A001248 a(n)=A000040(n)^(3-1)=A000040(n)^2, where 3 is the number of divisors 
               of a(n). - Omar E. Pol (info(AT)polprimos.com), May 06 2008
%F A001248 A000005(a(n))=3 or A002033(a(n))=2. - Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), 
               Oct 10 2009
%t A001248 Table[p=Prime[n]; p^2, {n, 1, 30}] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), 
               Aug 07 2008]
%o A001248 (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
%Y A001248 Cf. A000040, A049001, A024450.
%Y A001248 Cf. A008864, A060800.
%Y A001248 Cf. A000005, A002033. - Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), 
               Oct 10 2009
%Y A001248 Sequence in context: A082180 A068999 A077438 this_sequence A052043 A030146 
               A158146
%Y A001248 Adjacent sequences: A001245 A001246 A001247 this_sequence A001249 A001250 
               A001251
%K A001248 nonn,new
%O A001248 1,1
%A A001248 N. J. A. Sloane (njas(AT)research.att.com).

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