A378433 Dirichlet inverse of A325973, where A325973 is the arithmetic mean of {sum of unitary divisors} and {sum of squarefree divisors}.

1, -3, -4, 5, -6, 12, -8, -9, 9, 18, -12, -20, -14, 24, 24, 15, -18, -27, -20, -30, 32, 36, -24, 36, 20, 42, -24, -40, -30, -72, -32, -27, 48, 54, 48, 42, -38, 60, 56, 54, -42, -96, -44, -60, -54, 72, -48, -60, 35, -60, 72, -70, -54, 72, 72, 72, 80, 90, -60, 120, -62, 96, -72, 45, 84, -144, -68, -90, 96, -144, -72, -72

Offset: 1

Author

Antti Karttunen, Nov 26 2024

Keywords

• sign

Comments

Apparently differs from A378434 at positions given by A048111: 16, 32, 36, 48, 64, 72, 80, 81, 96, ...

Links

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

Crossrefs

Cf. A034448, A048111, A048250, A325973, A378434.

Programs

PARI

A325973(n) = (1/2)*sumdiv(n, d, d*(issquarefree(d) + (1==gcd(d, n/d))));
memoA378433 = Map();
A378433(n) = if(1==n,1,my(v); if(mapisdefined(memoA378433,n,&v), v, v = -sumdiv(n,d,if(dA325973(n/d)*A378433(d),0)); mapput(memoA378433,n,v); (v)));

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA325973(n/d) * a(d).