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A280559 Numbers m that divide Sum_{k=1..m} binomial(m,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
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
KEYWORD
nonn,more
AUTHOR
Paolo P. Lava, Jan 31 2017
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)