A280559 Numbers m that divide Sum_{k=1..m} binomial(m,k) mod k.

1, 14, 233, 244, 331, 889, 2725, 5219, 6746

Offset

1,2

Comments

Ratios are 0, 2, 44, 47, 58, 162, 529, 1004, 1318.

Links

Table of n, a(n) for n=1..9.

Example

C(14,1) mod 1 + C(14,2) mod 2 + ... + C(14,13) mod 13 + C(14,14) mod 14 = 0 + 1 + 1 + 1 + 2 + 3 + 2 + 3 + 4 + 1 + 1 + 7 + 1 + 1 = 28 and 28/14 = 2 so 14 is a term.

Maple

P:=proc(q) local k, n; for n from 1 to q do
if type(add(binomial(n, k) mod k, k=1..n)/n, integer) then print(n); fi; od; end: P(10^6);

Mathematica

Select[Range[10^3], Divisible[Sum[Mod[Binomial[#, k], k], {k, #}], #] &] (* Michael De Vlieger, Feb 07 2017 *)

Prog

(PARI) isok(n) = (sum(k=1, n, binomial(n, k) % k) % n) == 0; \\ Michel Marcus, Jul 16 2017

Crossrefs

Cf. A076541.

Sequence in context: A120048 A079563 A230346 * A305862 A222377 A220502

Adjacent sequences: A280556 A280557 A280558 * A280560 A280561 A280562

Keyword

nonn,more

Author

Paolo P. Lava, Jan 31 2017

Status

approved