A378525 Dirichlet inverse of A378542, where A378542 is the sum of divisors d of n such that n/d has an even number of prime factors (counted with multiplicity).

1, -2, -3, -1, -5, 5, -7, 2, -1, 9, -11, 5, -13, 13, 14, 0, -17, 5, -19, 7, 20, 21, -23, -5, -1, 25, 3, 9, -29, -20, -31, 0, 32, 33, 34, -4, -37, 37, 38, -9, -41, -30, -43, 13, 8, 45, -47, -2, -1, 7, 50, 15, -53, -5, 54, -13, 56, 57, -59, -28, -61, 61, 10, 0, 64, -50, -67, 19, 68, -56, -71, -7, -73, 73, 8, 21, 76

Offset: 1

Author

Antti Karttunen, Dec 01 2024

Keywords

• sign

Links

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

Crossrefs

Cf. A378542.

Cf. also A378526.

Programs

PARI

A378542(n) = sumdiv(n,d,d*!(bigomega(n/d)%2));
memoA378525 = Map();
A378525(n) = if(1==n,1,my(v); if(mapisdefined(memoA378525,n,&v), v, v = -sumdiv(n,d,if(dA378542(n/d)*A378525(d),0)); mapput(memoA378525,n,v); (v)));

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA378542(n/d) * a(d).