A140255 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

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

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

EXAMPLE

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.

PROG

(PARI)

expmangoldt(n)=ispower(n, , &n); if(isprime(n), n, 1);

a(n) = sumdiv(n, d, expmangoldt(d)) \\ Jodi Spitz, Apr 11 2023

CROSSREFS

Cf. A014963, A051731, A140254.

Cf. A140256.

Sequence in context: A004492 A360663 A333914 * A050270 A202307 A009041

Adjacent sequences: A140252 A140253 A140254 * A140256 A140257 A140258

KEYWORD

nonn

AUTHOR

Gary W. Adamson and Mats Granvik, May 16 2008

EXTENSIONS

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

STATUS

approved