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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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified June 6 14:04 EDT 2020. Contains 334827 sequences. (Running on oeis4.)