A378210 Dirichlet inverse of A191150, hypersigma variant 1.

1, -3, -4, -1, -6, 5, -8, 5, -1, 9, -12, 22, -14, 13, 14, 7, -18, 28, -20, 32, 20, 21, -24, -1, -1, 25, 11, 42, -30, 51, -32, -3, 32, 33, 34, -28, -38, 37, 38, -9, -42, 63, -44, 62, 49, 45, -48, -76, -1, 56, 50, 72, -54, -6, 54, -17, 56, 57, -60, -182, -62, 61, 63, -17, 64, 87, -68, 92, 68, 75, -72, -183, -74, 73

Offset: 1

Author

Antti Karttunen, Nov 22 2024

Keywords

• sign

Links

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

Crossrefs

Cf. A191150.

Cf. also A378211.

Programs

PARI

A191150(n) = (sigma(n)+sumdiv(n,d,if((d>1)&&(dA191150(d), 0)));
memoA378210 = Map();
A378210(n) = if(1==n,1,my(v); if(mapisdefined(memoA378210,n,&v), v, v = -sumdiv(n,d,if(dA191150(n/d)*A378210(d),0)); mapput(memoA378210,n,v); (v)));

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA191150(n/d) * a(d).