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A278963
a(n) is the number of k, 1<=k<=n, such that gcd(n,k) divides binomial(n,k).
1
1, 1, 2, 3, 4, 2, 6, 6, 8, 6, 10, 7, 12, 6, 8, 14, 16, 14, 18, 12, 14, 14, 22, 12, 24, 18, 24, 18, 28, 11, 30, 28, 26, 30, 26, 28, 36, 30, 30, 27, 40, 20, 42, 30, 32, 30, 46, 32, 48, 42, 32, 38, 52, 36, 46, 43, 50, 42, 58, 32, 60, 30, 52, 60, 50, 48, 66, 60, 50
OFFSET
1,3
COMMENTS
Length of row n of A278961.
a(n) is odd if and only if n = 1 or n is in A048618.
a(n) <= n-1 for n>1.
a(n) = n-1 if n is a prime or the square of a prime.
a(n) >= A000010(n).
LINKS
EXAMPLE
a(8) = 6 because gcd(8,k) divides binomial(8,k) for k=1,2,3,5,6,7 but not k=4 or k=8.
MAPLE
f:= proc(n, m) if binomial(n, m) mod igcd(n, m) = 0 then m else NULL fi end proc:
[seq(nops([seq(f(n, m), m=1..n)]), n=1..200)];
MATHEMATICA
a[n_] := Sum[Boole[Divisible[Binomial[n, k], GCD[n, k]]], {k, 1, n}];
Array[a, 100] (* Jean-François Alcover, Apr 29 2019 *)
PROG
(PARI) a(n) = sum(k=1, n, (binomial(n, k) % gcd(n, k))==0); \\ Michel Marcus, Dec 04 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Robert Israel, Dec 02 2016
STATUS
approved