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

1,4

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).

Formula

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

Prog

(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(d<n, A033879(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));

Crossrefs

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

Sequence in context: A155004 A176954 A034952 * A337549 A378755 A306456

Adjacent sequences: A378751 A378752 A378753 * A378755 A378763 A378767

Keyword

sign,new

Author

Antti Karttunen, Dec 11 2024

Status

approved