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

1,14

Links

Table of n, a(n) for n=1..100.

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

Prog

(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
(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

Crossrefs

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

Sequence in context: A179312 A076290 A198224 * A178109 A339873 A055672

Adjacent sequences: A178102 A178103 A178104 * A178106 A178107 A178108

Keyword

nonn

Author

Vladimir Shevelev, May 20 2010

Extensions

Corrected by R. J. Mathar, Sep 05 2011

Status

approved