A280559 Numbers m that divide Sum_{k=1..m} binomial(m,k) mod k.
1, 14, 233, 244, 331, 889, 2725, 5219, 6746, 61452, 101712
Offset: 1
Examples
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.
Crossrefs
Cf. A076541.
Programs
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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);
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Mathematica
Select[Range[10^3], Divisible[Sum[Mod[Binomial[#, k], k], {k, #}], #] &] (* Michael De Vlieger, Feb 07 2017 *) -
PARI
isok(n) = (sum(k=1, n, binomial(n,k) % k) % n) == 0; \\ Michel Marcus, Jul 16 2017
Extensions
a(10)-a(11) from Chai Wah Wu, Jul 22 2025
Comments