A158901 A051731 * (1, 1, 2, 3, 4, 5, ...).

1, 2, 3, 5, 5, 9, 7, 12, 11, 15, 11, 23, 13, 21, 21, 27, 17, 34, 19, 37, 29, 33, 23, 53, 29, 39, 37, 51, 29, 65, 31, 58, 45, 51, 45, 83, 37, 57, 53, 83, 41, 89, 43, 79, 73, 69, 47, 115, 55, 88, 69, 93, 53, 113, 69, 113, 77, 87, 59, 157, 61, 93, 99, 121, 81, 137, 67, 121, 93, 137

Offset: 1

Author

Gary W. Adamson, Mar 29 2009

Keywords

• nonn
• easy

Comments

a(n) = prime(n) if n is prime but nonprime n's can also have prime a(n).

Equals left border of triangle A158902.

Examples

			a(4) = 5 = (1, 1, 0, 1) dot (1, 1, 2, 3) = (1 + 1 + 0 + 3); where (1, 1, 0, 1) = row 4 of triangle A051731.
		

Crossrefs

Cf. A158902.

Programs

Maple

L := [1,seq(n, n=1..100)] ; read("transforms"); MOBIUSi(L) ; # R. J. Mathar, Apr 02 2009

PARI

a(n) = sigma(n) - numdiv(n) + 1; \\ Michel Marcus, Sep 14 2017

Formula

A051731 * [1, 1, 2, 3, 4, 5, ...] = inverse Mobius transform of [1, 1, 2, 3, 4, ...].

a(n) = sigma(n) - d(n) + 1. - Juri-Stepan Gerasimov, Aug 30 2009

a(n) = 1 + A065608(n). - R. J. Mathar, Jan 08 2015