login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A030514 a(n) = prime(n)^4. 111
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; text; internal format)
OFFSET
1,1
COMMENTS
Numbers with 5 divisors (1, p, p^2, p^3, p^4, where p is the n-th prime). - Alexandre Wajnberg, 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. - R. J. Mathar, Feb 01 2009
Except for the first three terms, all others are congruent to 1 mod 240. - Robert Israel, Aug 29 2014
LINKS
Eric Weisstein's World of Mathematics, Prime Power.
FORMULA
a(n) = A000040(n)^(5-1) = A000040(n)^4, where 5 is the number of divisors of a(n). - Omar E. Pol, May 06 2008
A000005(a(n)) = 5. - Alexandre Wajnberg, Jan 15 2006
A056595(a(n)) = 2. - Reinhard Zumkeller, Aug 15 2011
Sum_{n>=1} 1/a(n) = P(4) = 0.0769931397... (A085964). - Amiram Eldar, Jul 27 2020
From Amiram Eldar, Jan 23 2021: (Start)
Product_{n>=1} (1 + 1/a(n)) = zeta(4)/zeta(8) = 105/Pi^4 (A157290).
Product_{n>=1} (1 - 1/a(n)) = 1/zeta(4) = 90/Pi^4 (A215267). (End)
MAPLE
map(p -> p^4, select(isprime, [2, seq(2*i+1, i=1..100)])); # Robert Israel, Aug 29 2014
MATHEMATICA
Array[Prime[#]^4 &, 5!] (* Vladimir Joseph Stephan Orlovsky, Sep 01 2008 *)
PROG
(Sage)
[p**4 for p in prime_range(100)]
# Zerinvary Lajos, May 15 2007
(Magma) [NthPrime(n)^4: n in [1..100] ]; // Vincenzo Librandi, Apr 22 2011
(PARI) a(n)=prime(n)^4 \\ Charles R Greathouse IV, Mar 21 2013
(Haskell)
a030514 = (^ 4) . a000040
a030514_list = map (^ 4) a000040_list
-- Reinhard Zumkeller, Jun 03 2015
CROSSREFS
Cf. A258601.
Sequence in context: A366307 A113849 A046453 * A056571 A053909 A151502
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Description corrected by Eric W. Weisstein
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 19 03:33 EDT 2024. Contains 370952 sequences. (Running on oeis4.)