A378754 Dirichlet convolution of -A252748 and A323910.

1, 0, -1, -2, -1, -2, -3, -10, -10, -2, -1, -10, -3, -6, -5, -38, -1, -22, -3, -10, -11, -2, -5, -42, -14, -6, -60, -22, -1, -14, -5, -130, -5, -2, -11, -76, -3, -6, -11, -42, -1, -30, -3, -10, -36, -10, -5, -158, -46, -30, -5, -22, -5, -144, -5, -78, -11, -2, -1, -58, -5, -10, -64, -422, -11, -14, -3, -10, -17, -30

Offset: 1

Author

Antti Karttunen, Dec 11 2024

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Index entries for sequences related to prime indices in the factorization of n.
• Index entries for sequences related to sigma(n).

Crossrefs

Cf. A033879, A252748, A323910, A378755 (Dirichlet inverse).

Programs

PARI

A033879(n) = (n+n-sigma(n));
memoA323910 = Map();
A323910(n) = if(1==n,1,my(v); if(mapisdefined(memoA323910,n,&v), v, v = -sumdiv(n,d,if(dA033879(n/d)*A323910(d),0)); mapput(memoA323910,n,v); (v)));
A003961(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A252748(n) = (A003961(n) - (2*n));
A378754(n) = sumdiv(n,d,-A252748(d)*A323910(n/d));

Formula

a(n) = Sum_{d|n} -A252748(d)*A323910(n/d).