A378750 Dirichlet inverse of A377984, where A377984(n) = 2*sigma(n) - A003961(n).

1, -3, -3, 4, -5, 9, -5, 0, 8, 15, -11, -8, -11, 15, 17, 8, -17, -24, -17, -16, 21, 33, -19, 0, 12, 33, 24, -8, -29, -51, -27, 24, 35, 51, 31, 56, -35, 51, 39, 0, -41, -63, -41, -40, -28, 57, -43, 0, 32, -36, 53, -32, -49, -72, 57, 0, 57, 87, -59, 48, -57, 81, -4, 88, 61, -105, -65, -64, 67, -93, -71, 0, -69, 105

Offset: 1

Author

Antti Karttunen, Dec 09 2024

Keywords

• sign

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)

Crossrefs

Cf. A000203, A003961, A377984.

Cf. also A378749.

Programs

PARI

A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A377984(n) = (2*sigma(n) - A003961(n));
memoA378750 = Map();
A378750(n) = if(1==n,1,my(v); if(mapisdefined(memoA378750,n,&v), v, v = -sumdiv(n,d,if(dA377984(n/d)*A378750(d),0)); mapput(memoA378750,n,v); (v)));

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA377984(n/d) * a(d).