A140255 Inverse Mobius transform of A014963.

1, 3, 4, 5, 6, 7, 8, 7, 7, 9, 12, 10, 14, 11, 10, 9, 18, 11, 20, 12, 12, 15, 24, 13, 11, 17, 10, 14, 30, 15, 32, 11, 16, 21, 14, 15, 38, 23, 18, 15, 42, 17, 44, 18, 14, 27, 48, 16, 15, 15, 22, 20, 54, 15, 18, 17, 24, 33, 60, 20, 62, 35, 16, 13, 20, 21, 68, 24, 28, 19, 72, 19, 74

Offset: 1

Author

Gary W. Adamson and Mats Granvik, May 16 2008

Keywords

• nonn

Examples

			a(4) = 5 = (1, 1, 0, 1) dot (1, 2, 3, 2) = (1 + 2 + 0 + 2); where (1, 1, 0, 1) = row 4 of triangle A051731 and (1, 2, 3, 2) = the first 4 terms of A014963.
		

Links

• Jodi Spitz, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A014963, A051731, A140254.

Cf. A140256.

Programs

PARI

expmangoldt(n)=ispower(n, , &n); if(isprime(n), n, 1);
a(n) = sumdiv(n, d, expmangoldt(d)) \\ Jodi Spitz, Apr 11 2023

Formula

A051731 as an infinite lower triangular matrix * A014963 as a vector.

Equals row sums of triangle A140256. - Gary W. Adamson, May 16 2008

G.f.: Sum_{k>=1} M(k)*x^k/(1 - x^k), where M(k) is the exponential of Mangoldt function (A014963). - Ilya Gutkovskiy, Jan 16 2017

Extensions

More terms from R. J. Mathar, Jan 19 2009