A347382 a(n) = A252464(n) - A252464(A000593(n)).

0, 1, 0, 2, 0, 1, 1, 3, -3, 1, 1, 2, 1, 2, -1, 4, 3, -2, 3, 2, 0, 2, 4, 3, -7, 2, -2, 3, 5, 0, 6, 5, 0, 4, -1, -1, 3, 4, 0, 3, 7, 1, 7, 3, -3, 5, 9, 4, -4, -6, 2, 3, 11, -1, 0, 4, 2, 6, 11, 1, 6, 7, -3, 6, 0, 1, 10, 5, 3, 0, 14, 0, 8, 4, -8, 5, -1, 1, 15, 4, -1, 8, 16, 2, 2, 8, 4, 4, 18, -2, -1, 6, 5, 10, 2, 5, 19

Offset: 1

Author

Antti Karttunen, Aug 30 2021

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A000593, A001222, A061395, A252464, A347380, A347381.

Cf. also A347247, A347248.

Programs

Mathematica

f[p_, e_] := If[p == 2, 1, NextPrime[p, -1]^e]; g[1] = 1; g[n_] := Times @@ f @@@ FactorInteger[n]; h[1] = 0; h[n_] := h[n] = If[EvenQ[n], h[n/2] + 1, h[g[n]] + 1]; a[n_] := h[n] - h[DivisorSigma[1, n/2^IntegerExponent[n, 2]]]; Array[a, 100] (* Amiram Eldar, Sep 19 2021 *)

PARI

A000593(n) = sigma(n>>valuation(n, 2));
A252464(n) = if(1==n,0,(bigomega(n) + A061395(n) - 1));
A347382(n) = (A252464(n)-A252464(A000593(n)));

Formula

For all n >= 0, a(2^n) = n.