A378643 Dirichlet inverse of A103977.

1, -1, -2, 0, -4, 4, -6, 0, -1, 6, -10, -2, -12, 8, 10, 0, -16, -3, -18, 0, 14, 12, -22, 0, -3, 14, -2, 2, -28, -28, -30, 0, 22, 18, 26, 8, -36, 20, 26, -2, -40, -36, -42, 2, 4, 24, -46, 0, -5, -1, 34, 2, -52, 4, 42, -4, 38, 30, -58, 18, -60, 32, 6, 0, 50, -52, -66, 2, 46, -44, -70, -4, -72, 38, 2, 2, 62, -60, -78, 0

Offset: 1

Author

Antti Karttunen, Dec 03 2024

Keywords

• sign

Links

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

Crossrefs

Dirichlet inverse of A103977.

Cf. A005101, A263837, A323910, A378645, A378646, A378647.

Programs

PARI

memoA378643 = Map();
A378643(n) = if(1==n,1,my(v); if(mapisdefined(memoA378643,n,&v), v, v = -sumdiv(n,d,if(dA103977(n/d)*A378643(d),0)); mapput(memoA378643,n,v); (v)));

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA103977(n/d) * a(d).

a(n) = A323910(n) when n is a non-abundant number (A263837), and also for some of the abundant numbers, A005101.