A355826 - OEIS

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A355826

Dirichlet inverse of A355825, characteristic function of exponentially odious numbers.

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, 1, 0, -1, -1, -1, 2, 1, 1, 1, 0, -1, 1, 1, -1, -1, -1, -1, 0, 0, 1, -1, 2, 0, 0, 1, 0, -1, -1, 1, -1, 1, 1, -1, 0, -1, 1, 0, 0, 1, -1, -1, 0, 1, -1, -1, 0, -1, 1, 0, 0, 1, -1, -1, 2, -2, 1, -1, 0, 1, 1, 1, -1, -1, 0, 1, 0, 1, 1, 1, -2, -1, 0, 0, 0, -1, -1, -1, -1, -1, 1, -1, 0, -1, -1, 1, 2, -1, -1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, -1, -4

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OFFSET

1,16

COMMENTS

Multiplicative because A355825 is.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..100000

Index entries for sequences computed from exponents in factorization of n

FORMULA

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A355825(n/d) * a(d).

MATHEMATICA

s[n_] := If[AllTrue[FactorInteger[n][[;; , 2]], OddQ[DigitCount[#, 2, 1]] &], 1, 0]; a[1] = 1; a[n_] := a[n] = -DivisorSum[n, s[n/#]*a[#] &, # < n &]; Array[a, 100] (* Amiram Eldar, Jul 19 2022 *)

PROG

(PARI)

A355825(n) = factorback(apply(e->(hammingweight(e)%2), factor(n)[, 2]));

memoA355826 = Map();

A355826(n) = if(1==n, 1, my(v); if(mapisdefined(memoA355826, n, &v), v, v = -sumdiv(n, d, if(d<n, A355825(n/d)*A355826(d), 0)); mapput(memoA355826, n, v); (v)));

CROSSREFS

Cf. A270428, A355825.

Differs from related A355824 for the first time at n=128, where a(128) = -4, while A355824(128) = -3.

Cf. also A355819.

Sequence in context: A280269 A321894 A355824 * A355819 A330262 A098055

Adjacent sequences: A355823 A355824 A355825 * A355827 A355828 A355829

KEYWORD

sign,mult

AUTHOR

Antti Karttunen, Jul 19 2022

STATUS

approved