login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation to keep the OEIS running. In 2018 we replaced the server with a faster one, added 20000 new sequences, and reached 7000 citations (often saying "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A030514 a(n) = prime(n)^4. 72
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

Solutions of the equation n' = 4*n^(3/4), where n' is the arithmetic derivative of n. - Paolo P. Lava, Oct 31 2012

Except for the first three terms, all others are congruent to 1 mod 240. - Robert Israel, Aug 29 2014

LINKS

R. J. Mathar, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Prime Power.

OEIS Wiki, Index entries for number of divisors

Index to sequences related to prime signature

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

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) BB = primes_first_n(36) list = [] for i in range(36): list.append(BB[i]^4) list # 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. A030078, A131991, A131992, A000005, A000040, A001248.

Cf. A258601.

Sequence in context: A153157 A113849 A046453 * A056571 A053909 A151502

Adjacent sequences:  A030511 A030512 A030513 * A030515 A030516 A030517

KEYWORD

nonn,easy

AUTHOR

Jeff Burch

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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 18 18:07 EST 2018. Contains 318243 sequences. (Running on oeis4.)