A349342 Sum of A026741 and its Dirichlet inverse.

2, 0, 0, 1, 0, 6, 0, 3, 9, 10, 0, 9, 0, 14, 30, 7, 0, 9, 0, 15, 42, 22, 0, 15, 25, 26, 27, 21, 0, 0, 0, 15, 66, 34, 70, 18, 0, 38, 78, 25, 0, 0, 0, 33, 45, 46, 0, 27, 49, 25, 102, 39, 0, 27, 110, 35, 114, 58, 0, 15, 0, 62, 63, 31, 130, 0, 0, 51, 138, 0, 0, 36, 0, 74, 75, 57, 154, 0, 0, 45, 81, 82, 0, 21, 170, 86

Offset: 1

Author

Antti Karttunen, Nov 15 2021

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A026741, A349341.

Programs

PARI

A026741(n) = if(n%2,n,n/2);
A349341(n) = { my(f = factor(n)); prod(i=1, #f~, if(2==f[i,1], -1, if(1==f[i,2], -f[i,1], 0))); };
A349342(n) = (A026741(n)+A349341(n));

Formula

a(n) = A026741(n) + A349341(n).

a(1) = 2, and for n > 1, a(n) = -Sum_{d|n, 1A026741(d) * A349341(n/d).