A138403 a(n) = p^3*(p-1), where p = prime(n).

8, 54, 500, 2058, 13310, 26364, 78608, 123462, 267674, 682892, 893730, 1823508, 2756840, 3339294, 4775858, 7741604, 11911982, 13618860, 19850358, 25053770, 28009224, 38457042, 46886534, 62037272, 87616608, 103030100, 111458154

Offset: 1

Author

Artur Jasinski, Mar 19 2008

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..200
• Index to sequences related to prime powers.

Crossrefs

Cf. A000010, A030514, A030078, A065415.

Programs

Magma

[NthPrime((n))^4 - NthPrime((n))^3: n in [1..40] ]; // Vincenzo Librandi, Jun 17 2011

Mathematica

a = {}; Do[p = Prime[n]; AppendTo[a, p^4 - p^3], {n, 1, 50}]; a

PARI

forprime(p=2,1e3,print1(p^4-p^3", ")) \\ Charles R Greathouse IV, Jun 16 2011

Formula

a(n) = A000010(prime(n)^4). - R. J. Mathar, Oct 15 2017

From Amiram Eldar, Nov 22 2022: (Start)

a(n) = prime(n)^4 - prime(n)^3 = A030514(n) - A030078(n).

Product_{n>=1} (1 - 1/a(n)) = A065415. (End)

Sum_{n>=1} 1/a(n) = A382551. - R. J. Mathar, Mar 31 2025