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A280559 Numbers n such that n divides Sum_{k=1..n} binomial(n,k) mod k. 1
1, 14, 233, 244, 331, 889, 2725, 5219, 6746 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 19 04:40 EDT 2019. Contains 328211 sequences. (Running on oeis4.)