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

Author

Ryan Propper, Aug 08 2005

Keywords

• base
• hard
• nonn

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.

Examples

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

Programs

Mathematica

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

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

Extensions

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