A354186 Dirichlet inverse of A348717.

1, -2, -2, 0, -2, 2, -2, 0, 0, -2, -2, 4, -2, -6, 2, 0, -2, -2, -2, 12, -2, -14, -2, 0, 0, -18, 0, 20, -2, 10, -2, 0, -6, -26, 2, 8, -2, -30, -14, 0, -2, 30, -2, 36, 4, -38, -2, 0, 0, -18, -18, 44, -2, -6, -2, 0, -26, -50, -2, -4, -2, -54, 12, 0, -6, 54, -2, 60, -30, 2, -2, -8, -2, -66, -2, 68, 2, 90, -2, 0, 0, -74

Offset: 1

Author

Antti Karttunen, May 19 2022

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A348717, A354187.

Programs

PARI

A348717(n) = if(1==n, 1, my(f = factor(n), k = primepi(f[1, 1])-1); for (i=1, #f~, f[i, 1] = prime(primepi(f[i, 1])-k)); factorback(f));
memoA354186 = Map();
A354186(n) = if(1==n,1,my(v); if(mapisdefined(memoA354186,n,&v), v, v = -sumdiv(n,d,if(dA348717(n/d)*A354186(d),0)); mapput(memoA354186,n,v); (v)));

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d < n} A348717(n/d) * a(d).

a(n) = A354187(n) - A348717(n).