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

1,3

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

Robert Israel, Table of n, a(n) for n = 1..10000

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

Cf. A000010, A048618, A278961.

Sequence in context: A061020 A206369 A152958 * A308085 A178970 A172054

Adjacent sequences: A278960 A278961 A278962 * A278964 A278965 A278966

Keyword

nonn

Author

Robert Israel, Dec 02 2016

Status

approved