A355819 Dirichlet inverse of A270419, denominator of the rational number obtained when the exponents in prime factorization of n are reinterpreted as alternating binary sums (A065620).

1, -1, -1, 0, -1, 1, -1, -1, 0, 1, -1, 0, -1, 1, 1, 2, -1, 0, -1, 0, 1, 1, -1, 1, 0, 1, -2, 0, -1, -1, -1, -8, 1, 1, 1, 0, -1, 1, 1, 1, -1, -1, -1, 0, 0, 1, -1, -2, 0, 0, 1, 0, -1, 2, 1, 1, 1, 1, -1, 0, -1, 1, 0, 12, 1, -1, -1, 0, 1, -1, -1, 0, -1, 1, 0, 0, 1, -1, -1, -2, 4, 1, -1, 0, 1, 1, 1, 1, -1, 0, 1, 0, 1, 1, 1, 8

Offset: 1

Author

Antti Karttunen, Jul 19 2022

Keywords

• sign
• mult

Comments

Multiplicative because A270419 is.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16383
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000

Crossrefs

Cf. A065620, A270419.

Cf. also A355826.

Programs

PARI

A065620(n, c=1) = sum(i=0, logint(n+!n, 2), if(bittest(n, i), (-1)^c++<A065620
A270419(n) = {n=factor(n); n[, 2]=apply(A065620, n[, 2]); denominator(factorback(n)); }; \\ From A270419
memoA355819 = Map();
A355819(n) = if(1==n,1,my(v); if(mapisdefined(memoA355819,n,&v), v, v = -sumdiv(n,d,if(dA270419(n/d)*A355819(d),0)); mapput(memoA355819,n,v); (v)));

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA270419(n/d) * a(d).