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A355692
Dirichlet inverse of A355442, gcd(A003961(n), A276086(n)), where A003961 is fully multiplicative with a(p) = nextprime(p), and A276086 is primorial base exp-function.
2
1, -3, -1, 0, -1, 1, -1, 24, -4, 3, -1, 16, -1, 3, -3, -72, -1, 6, -1, 6, -3, 3, -1, -68, 0, 3, -116, 0, -1, 21, -1, 24, 1, 3, -5, 72, -1, 3, -3, -120, -1, 23, -1, 6, -158, 3, -1, 28, 0, -18, -3, 0, -1, 632, -5, -24, -3, 3, -1, -54, -1, 3, 16, 504, -5, -1, -1, 6, -3, 15, -1, -400, -1, 3, -236, 0, 1, 23, -1, 474, 136
OFFSET
1,2
FORMULA
a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A355442(n/d) * a(d).
PROG
(PARI)
A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A355442(n) = gcd(A003961(n), A276086(n));
memoA355692 = Map();
A355692(n) = if(1==n, 1, my(v); if(mapisdefined(memoA355692, n, &v), v, v = -sumdiv(n, d, if(d<n, A355442(n/d)*A355692(d), 0)); mapput(memoA355692, n, v); (v)));
CROSSREFS
KEYWORD
sign
AUTHOR
Antti Karttunen, Jul 18 2022
STATUS
approved