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

1,16

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

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A270419(n/d) * a(d).

Prog

(PARI)
A065620(n, c=1) = sum(i=0, logint(n+!n, 2), if(bittest(n, i), (-1)^c++<<i)); \\ From 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(d<n, A270419(n/d)*A355819(d), 0)); mapput(memoA355819, n, v); (v)));

Crossrefs

Cf. A065620, A270419.

Cf. also A355826.

Sequence in context: A321894 A355824 A355826 * A330262 A098055 A344739

Adjacent sequences: A355816 A355817 A355818 * A355820 A355821 A355822

Keyword

sign,mult

Author

Antti Karttunen, Jul 19 2022

Status

approved