A135177 a(n) = p^2*(p-1), where p = prime(n).

4, 18, 100, 294, 1210, 2028, 4624, 6498, 11638, 23548, 28830, 49284, 67240, 77658, 101614, 146068, 201898, 223260, 296274, 352870, 383688, 486798, 564898, 697048, 903264, 1020100, 1082118, 1213594, 1283148, 1430128, 2032254, 2230930

Offset

1,1

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000 (first 1000 terms from Vincenzo Librandi)

Index to sequences related to prime powers.

Formula

a(n) = p^3 - p^2 = A030078(n) - A001248(n).

a(n) = A000010(prime(n)^3). - R. J. Mathar, Oct 15 2017

Sum_{n>=1} 1/a(n) = A152441. - Amiram Eldar, Nov 09 2020

From Amiram Eldar, Nov 22 2022: (Start)

Product_{n>=1} (1 + 1/a(n)) = A065483.

Product_{n>=1} (1 - 1/a(n)) = A065414. (End)

a(n) = 2*A138416(n). - Antti Karttunen, Dec 14 2024

Example

a(4) = 294 because the 4th prime number is 7, 7^2 = 49, 7-1 = 6 and 49 * 6 = 294.

Mathematica

Table[Prime[n]^3-Prime[n]^2, {n, 1, 12}] (* Vladimir Joseph Stephan Orlovsky, Apr 29 2008 *)
Table[p^3-p^2, {p, Prime[Range[40]]}] (* Harvey P. Dale, Jan 15 2015 *)

Prog

(Magma)[(p^3-p^2): p in PrimesUpTo(200)]; // Vincenzo Librandi, Dec 15 2010
(PARI) forprime(p=2, 1e3, print1(p^2*(p-1)", ")) \\ Charles R Greathouse IV, Jun 16 2011
(PARI) A135177(n) = eulerphi(prime(n)^3); \\ Antti Karttunen, Dec 14 2024
(PARI) A135177(n) = ((p->(p-1)*p*p)(prime(n))); \\ Antti Karttunen, Dec 14 2024

Crossrefs

Cf. A001248 (p^2), A030078 (p^3), A045991 (n^2 * (n-1)), A065414, A065483, A138416 (terms halved), A152441.

Column 4 of A379010.

Sequence in context: A263688 A197593 A084832 * A244309 A137958 A371543

Adjacent sequences: A135174 A135175 A135176 * A135178 A135179 A135180

Keyword

nonn,easy

Author

Omar E. Pol, Nov 25 2007

Status

approved