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

1,4

Links

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

Formula

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

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

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

Prog

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

Crossrefs

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

Sequence in context: A153846 A284383 A072406 * A364464 A120680 A360104

Adjacent sequences: A297114 A297115 A297116 * A297118 A297119 A297120

Keyword

nonn

Author

Antti Karttunen, Dec 26 2017

Status

approved