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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 23 17:33 EST 2022. Contains 350514 sequences. (Running on oeis4.)