A278963 a(n) is the number of k, 1<=k<=n, such that gcd(n,k) divides binomial(n,k).
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
Keywords
Examples
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.
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
-
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 *) -
PARI
a(n) = sum(k=1, n, (binomial(n, k) % gcd(n, k))==0); \\ Michel Marcus, Dec 04 2016
Comments