A324100 A000120-deficiency of n permuted by A156552: a(n) = A192895(A156552(n)).

-1, 0, -1, 1, -1, 2, -2, 2, 1, 3, -2, 4, -1, 2, 1, 5, -2, 6, -2, 6, 4, 7, -3, 5, 4, 2, 3, 8, 3, 9, -4, 2, 5, 5, 1, 10, -1, 12, 2, 11, -2, 12, -2, 2, 19, 13, -4, 8, 0, 12, -2, 14, -3, 11, -3, 14, 12, 15, -3, 16, 7, 2, 5, 5, 4, 17, 4, 2, -2, 18, 1, 19, 6, 2, 5, 8, 4, 20, -4, 10, 8, 21, 8, 20, 24, 42, 15, 22, 7, 16, 6, 28, 45, 20, 0, 23, 1, 12, 1

Offset: 2

Author

Antti Karttunen, Feb 19 2019

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 2..4473
• Index entries for sequences related to binary expansion of n
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A000120, A156552, A192895, A324113 (sign of each term).

Cf. A324101, A324102 (positions of nonnegative and negative terms).

Cf. also A324114, A324194.

Programs

PARI

A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
A156552(n) = if(1==n, 0, if(!(n%2), 1+(2*A156552(n/2)), 2*A156552(A064989(n))));
A192895(n) = sumdiv(n, d, hammingweight(d)*(-1)^(d==n));
A324100(n) = A192895(A156552(n));

Formula

a(n) = A192895(A156552(n)).