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A030514
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4th powers of primes.
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45
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16, 81, 625, 2401, 14641, 28561, 83521, 130321, 279841, 707281, 923521, 1874161, 2825761, 3418801, 4879681, 7890481, 12117361, 13845841, 20151121, 25411681, 28398241, 38950081, 47458321, 62742241, 88529281, 104060401, 112550881, 131079601, 141158161
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Unique numbers having 5 divisors (1, p, p^2, p^3, p^4, where p is the n-th prime). - Alexandre Wajnberg (alexandre.wajnberg(AT)skynet.be), Jan 15 2006
Subsequence of A036967. - Reinhard Zumkeller, Feb 05 2008
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
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, Feb 01 2009]
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LINKS
| R. J. Mathar, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
OEIS Wiki, Index entries for number of divisors
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FORMULA
| 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
A000005(a(n))=5. Juri-Stepan Gerasimov, Oct 10 2009
A056595(a(n)) = 2. [Reinhard Zumkeller, Aug 15 2011]
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MATHEMATICA
| Array[Prime[ # ]^4&, 5! ] (* From Vladimir Orlovsky, Sep 01 2008 *)
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PROG
| (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
(MAGMA) [NthPrime(n)^4: n in [1..100] ]; // Vincenzo Librandi, Apr 22 2011
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CROSSREFS
| Cf. A030078, A131991, A131992.
Cf. A000005, A000040, A001248.
Sequence in context: A153157 A113849 A046453 * A056571 A053909 A151502
Adjacent sequences: A030511 A030512 A030513 * A030515 A030516 A030517
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KEYWORD
| nonn,easy
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AUTHOR
| Jeff Burch (jmburch(AT)osprey.smcm.edu)
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EXTENSIONS
| Description corrected by Eric Weisstein (eric(AT)weisstein.com)
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