A378432 Dirichlet inverse of A296075, where A296075 is the sum of deficiencies of divisors of n.

1, -2, -3, 1, -5, 8, -7, 0, 1, 12, -11, -3, -13, 16, 17, 0, -17, -4, -19, -5, 23, 24, -23, 2, 1, 28, -1, -7, -29, -44, -31, 0, 35, 36, 37, 5, -37, 40, 41, 2, -41, -60, -43, -11, -7, 48, -47, 4, 1, -8, 53, -13, -53, 0, 57, 2, 59, 60, -59, 25, -61, 64, -9, 0, 67, -92, -67, -17, 71, -92, -71, 6, -73, 76, -9, -19, 79

Offset: 1

Author

Antti Karttunen, Nov 26 2024

Keywords

• sign

Links

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

Crossrefs

Cf. A033879.

Dirichlet inverse of A296075.

Möbius transform of A323910.

Programs

PARI

A033879(n) = ((2*n)-sigma(n));
A296075(n) = sumdiv(n,d,A033879(d));
memoA378432 = Map();
A378432(n) = if(1==n,1,my(v); if(mapisdefined(memoA378432,n,&v), v, v = -sumdiv(n,d,if(dA296075(n/d)*A378432(d),0)); mapput(memoA378432,n,v); (v)));

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA296075(n/d) * a(d).