A138664 a(n) = number of positive integers k, k <= n, where the number of one's in the binary representation of each k divides n.

1, 2, 2, 4, 3, 6, 3, 7, 5, 9, 4, 12, 4, 10, 8, 12, 5, 17, 5, 15, 11, 14, 5, 24, 5, 15, 14, 18, 5, 25, 5, 21, 16, 18, 7, 35, 6, 19, 19, 27, 6, 35, 6, 27, 23, 20, 6, 46, 6, 23, 24, 31, 6, 40, 9, 33, 26, 21, 6, 60, 6, 21, 26, 37, 13, 45, 7, 40, 29, 31, 7, 66, 7, 26, 38, 43, 7, 53, 7, 53, 34

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

The integers 1 through 9 in binary are (1, 10, 11, 100, 101, 110, 111, 1000, 1001). So the numbers of 1's in these binary representations form the sequence (1,1,2,1,2,2,3,1,2) (the first 9 terms of sequence A000120, starting from A000120(1)). 9 is divisible by all the 1's (there are 4 of those) and by the one 3. So a(9) = 4+1 = 5.

Mathematica

a[n_] := Sum[Boole[Divisible[n, DigitCount[k, 2, 1]]], {k, 1, n}]; Array[a, 100] (* Amiram Eldar, Jul 16 2023 *)

Crossrefs

Cf. A138663, A000120.

Sequence in context: A089173 A126090 A058266 * A140357 A352622 A089265

Adjacent sequences: A138661 A138662 A138663 * A138665 A138666 A138667

Keyword

nonn,base

Author

Leroy Quet, Mar 25 2008

Extensions

Corrected and extended by Sean A. Irvine, Oct 12 2009

Status

approved