Search: id:A030514
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%I A030514
%S A030514 16,81,625,2401,14641,28561,83521,130321,279841,707281,923521,
%T A030514 1874161,2825761,3418801,4879681,7890481,12117361,13845841,20151121,
%U A030514 25411681,28398241,38950081,47458321,62742241,88529281,104060401
%N A030514 4th powers of primes.
%C A030514 Unique numbers having 5 divisors (1, n-th prime, n-th prime^2=their square 
               root, n-th prime^3, themselves). - Alexandre Wajnberg (alexandre.wajnberg(AT)skynet.be), 
               Jan 15 2006
%C A030514 Subsequence of A036967. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Feb 05 2008
%C A030514 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 A030514 The general product formula for even s is: product_{p=A000040} (p^s-1)/
               (p^s+1)= 2*Bernoulli(2s)/( binomial(2s,s)*Bernoulli^2(s)), where 
               the infinite product is over all primes. Here, with s=4, product_{n=1,
               2,...} (a(n)-1)/(a(n)+1) = 6/7. In A030516, where s=6, the product 
               of the ratios is 691/715. For s=8, the 8th row in A120458, the corresponding 
               product of ratios is 7234/7293. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Feb 01 2009]
%H A030514 R. J. Mathar, <a href="b030514.txt">Table of n, a(n) for n = 1..457</
               a>
%H A030514 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 A030514 a(n)=A000040(n)^(5-1)=A000040(n)^4, where 5 is the number of divisors 
               of a(n). - Omar E. Pol (info(AT)polprimos.com), May 06 2008
%F A030514 A000005(a(n))=5. Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Oct 10 
               2009
%t A030514 Array[Prime[ # ]^4&, 5! ] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), 
               Sep 01 2008]
%o A030514 (SAGE) BB = primes_first_n(36) list = [] for i in range(36): list.append(BB[i]^4) 
               list - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 15 2007
%Y A030514 Cf. A030078, A131991, A131992.
%Y A030514 Cf. A000005, A000040.
%Y A030514 Sequence in context: A153157 A113849 A046453 this_sequence A056571 A053909 
               A151502
%Y A030514 Adjacent sequences: A030511 A030512 A030513 this_sequence A030515 A030516 
               A030517
%K A030514 nonn,easy
%O A030514 1,1
%A A030514 Jeff Burch (jmburch(AT)osprey.smcm.edu)
%E A030514 Description corrected by Eric Weisstein (eric(AT)weisstein.com)

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