OFFSET

1,2

COMMENTS

All the odd numbers are terms. - Amiram Eldar, Aug 24 2024

LINKS

Ivan Neretin, Table of n, a(n) for n = 1..10000

EXAMPLE

For n = 12, binomial(12,6) = 924 = 12*77 is divisible by 12, so 12 is in the sequence.

For n = 13, binomial(13,6) = 1716 = 13*132 is divisible by 13, so 13 is in the sequence.

From David A. Corneth, Apr 22 2018: (Start)

For n = 20, we wonder if 20 = 2^2 * 5 divides binomial(20, 10) = 20! / (10!)^2.

The exponent of 2 in the prime factorization of 20! is 10 + 5 + 2 + 1 = 18.

The exponent of 2 in the prime factorization of 10! is 5 + 2 + 1 = 8.

Therefore, the exponent of 2 in binomial(20, 10) is 18 - 2*8 = 2.

The exponent of 5 in the prime factorization of 20! is 4.

The exponent of 5 in the prime factorization of 10! is 2.

Therefore, exponent of 5 in binomial(20, 10) is 4 - 2*2 = 0.

So binomial(20, 10) is not divisible by 20, and 20 is not in the sequence. (End)

MATHEMATICA

Select[Range[150], Divisible[Binomial[#, Floor[#/2]], #]&] (* Harvey P. Dale, Sep 15 2011 *)

PROG

(PARI) isok(n) = (binomial(n, n\2) % n) == 0; \\ Michel Marcus, Apr 22 2018

CROSSREFS

KEYWORD

nonn

AUTHOR

STATUS

approved