A109711 Numbers n such that the sum of the binary digits of n! is divisible by n.

1, 12, 78, 87, 292, 362, 1375, 1387, 1408, 1430, 1445, 88664, 355390, 356630, 1420936, 1423614, 1428922

Offset

1,2

Comments

Next term after 1445 is greater than 25000. - Robert G. Wilson v, Aug 08 2005

The quotient (sum of binary digits)/n is 1, 1, 2, 2, 3, 3, 4, 4, 4, 4, 4, 7, 8, 8, 9, 9, 9.

Links

Table of n, a(n) for n=1..17.

Example

The binary digits of 1445! sum to 5780 and 5780 is divisible by 1445, so 1445 is in the sequence.

Mathematica

Do[k = n!; s = Plus @@ IntegerDigits[k, 2]; If[Mod[s, n] == 0, Print[n]], {n, 1, 10^4}]

Prog

(PARI) is(n)=my(v=binary(n!)); sum(i=1, #v, v[i])%n==0 \\ Charles R Greathouse IV, Jun 24 2011
(PARI) is(n)=hammingweight(n!)%n==0 \\ Charles R Greathouse IV, Mar 28 2013

Crossrefs

Sequence in context: A026964 A026974 A210695 * A244390 A136540 A139612

Adjacent sequences: A109708 A109709 A109710 * A109712 A109713 A109714

Keyword

base,hard,nonn

Author

Ryan Propper, Aug 08 2005

Extensions

a(12)-a(17) from Lars Blomberg, Jun 24 2011

Status

approved