A297117 Möbius transform of A011371, n minus (number of 1's in binary expansion of n).

0, 1, 1, 2, 3, 2, 4, 4, 6, 4, 8, 4, 10, 6, 7, 8, 15, 6, 16, 8, 13, 10, 19, 8, 19, 12, 16, 12, 25, 8, 26, 16, 22, 16, 25, 12, 34, 18, 24, 16, 38, 12, 39, 20, 24, 22, 42, 16, 42, 20, 31, 24, 49, 18, 39, 24, 36, 28, 54, 16, 56, 30, 33, 32, 50, 20, 64, 32, 46, 24, 67, 24, 70, 36, 41, 36, 61, 24, 74, 32, 55, 40, 79, 24

Offset: 1

Author

Antti Karttunen, Dec 26 2017

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A000010, A000120, A008683, A011371, A051953, A297111, A297114, A297115.

Programs

PARI

A297117(n) = sumdiv(n,d,moebius(n/d)*(d-hammingweight(d)));

Formula

a(n) = Sum_{d|n} A008683(n/d) * (d - A000120(d)).

a(n) = A297111(n) - A000010(n).

a(n) = A297114(n) + A051953(n).