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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.
5
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
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
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, May 20 2010
EXTENSIONS
Corrected by R. J. Mathar, Sep 05 2011
STATUS
approved