A036690 Product of a prime and the following number.

6, 12, 30, 56, 132, 182, 306, 380, 552, 870, 992, 1406, 1722, 1892, 2256, 2862, 3540, 3782, 4556, 5112, 5402, 6320, 6972, 8010, 9506, 10302, 10712, 11556, 11990, 12882, 16256, 17292, 18906, 19460, 22350, 22952, 24806, 26732, 28056, 30102

Offset

1,1

Comments

The infinite sum over the reciprocals is given in A179119. - Wolfdieter Lang, Jul 10 2019

1/a(n) is the asymptotic density of numbers whose prime(n)-adic valuation is positive and even. - Amiram Eldar, Jan 23 2021

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Formula

a(n) = prime(n)*(prime(n)+1).

a(n) = A060800(n) - 1.

a(n) = 2*A034953(n). - Artur Jasinski, Feb 06 2007

From Amiram Eldar, Jan 23 2021: (Start)

Product_{n>=1} (1 + 1/a(n)) = zeta(2)/zeta(3) (A306633).

Product_{n>=1} (1 - 1/a(n)) = A065463. (End)

Example

a(3)=30 because prime(3)=5 and prime(3)+1=6, hence 5*6 = 30.

Mathematica

Table[(Prime[n] + 1) Prime[n], {n, 1, 100}] (* Artur Jasinski, Feb 06 2007 *)

Prog

(Magma)[p^2+p: p in PrimesUpTo(250)]; // Vincenzo Librandi, Dec 19 2010
(PARI) a(n)=my(p=prime(n)); p*(p+1) \\ Charles R Greathouse IV, Mar 27 2020

Crossrefs

Cf. A036689, A034953, A065463, A179119, A306633.

Sequence in context: A071342 A125056 A011987 * A229746 A256579 A357197

Adjacent sequences: A036687 A036688 A036689 * A036691 A036692 A036693

Keyword

nonn,easy

Author

Felice Russo

Status

approved