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A280559
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Numbers m that divide Sum_{k=1..m} binomial(m,k) mod k.
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1
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OFFSET
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1,2
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COMMENTS
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Ratios are 0, 2, 44, 47, 58, 162, 529, 1004, 1318.
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LINKS
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EXAMPLE
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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.
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MAPLE
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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
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Select[Range[10^3], Divisible[Sum[Mod[Binomial[#, k], k], {k, #}], #] &] (* Michael De Vlieger, Feb 07 2017 *)
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PROG
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(PARI) isok(n) = (sum(k=1, n, binomial(n, k) % k) % n) == 0; \\ Michel Marcus, Jul 16 2017
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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