A355694 Dirichlet inverse of A277791, denominator of sum of reciprocals of proper divisors of n.

1, -1, -1, -1, -1, -4, -1, -1, -2, -8, -1, 9, -1, -12, -13, -1, -1, 6, -1, 1, -19, -20, -1, -10, -4, -24, -4, 1, -1, 26, -1, -1, -31, -32, -33, 27, -1, -36, -37, 10, -1, 34, -1, 1, -12, -44, -1, 35, -6, 2, -49, 1, -1, -14, -53, 62, -55, -56, -1, 87, -1, -60, -18, -1, -63, 110, -1, 1, -67, 42, -1, -57, -1, -72, 12

Offset: 1

Author

Antti Karttunen, Jul 18 2022

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..12000
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Crossrefs

Cf. A277791.

Programs

PARI

A277791(n) = denominator((sigma(n)-1)/n); \\ From A277791
memoA355694 = Map();
A355694(n) = if(1==n,1,my(v); if(mapisdefined(memoA355694,n,&v), v, v = -sumdiv(n,d,if(dA277791(n/d)*A355694(d),0)); mapput(memoA355694,n,v); (v)));

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA277791(n/d) * a(d).