

A109711


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


1



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



