A178105 Let B_n be the set of divisors 2 <= d <= n/2 of binomial(n-d-1,d-1) such that gcd(n,d)>1. The sequence lists the minimal d of B_n, or a(n)=0 if B_n is empty.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 6, 0, 6, 0, 0, 0, 4, 0, 0, 0, 6, 6, 10, 0, 4, 0, 6, 0, 6, 0, 14, 0, 4, 9, 6, 0, 8, 0, 8, 6, 4, 0, 10, 0, 6, 15, 12, 0, 4, 20, 6, 18, 6, 0, 18, 0, 4, 6, 6, 10, 9, 0, 14, 9, 4, 0, 6, 0, 6, 12, 8, 21, 4, 0, 6, 6, 6, 0, 16, 20, 4, 18, 6, 0, 6, 28, 10, 9, 4, 15, 9, 0, 6, 6, 14

Offset: 1

Author

Vladimir Shevelev, May 20 2010

Keywords

• nonn

Links

• Vladimir Shevelev, On divisibility of binomial(n-i-1,i-1) by i, Intl. J. of Number Theory, 3, no.1 (2007), 119-139.

Crossrefs

Cf. A138389, A178071, A178098, A178099, A178100, A178101, A178109, A178110.

Programs

PARI

a(n) = {my(md = -1); for (d=2, n\2, if (((binomial(n-d-1,d-1) % d) == 0) && (gcd(n, d) > 1), if (md == -1, md = d, md = min(d, md)));); if (md == -1, 0, md);} \\ Michel Marcus, Feb 07 2016

Sage

def A178105(n):
    return next((d for d in (2..n//2) if binomial(n-d-1,d-1) % d == 0 and gcd(n,d) > 1), 0)
# D. S. McNeil, Sep 05 2011

Extensions

Corrected by R. J. Mathar, Sep 05 2011