cp's OEIS Frontend

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.

%I A178105 #25 Feb 26 2020 15:15:49
%S A178105 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,
%T A178105 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,
%U A178105 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
%N 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.
%H A178105 Vladimir Shevelev, <a href="http://dx.doi.org/10.1142/S179304210700078X">On divisibility of binomial(n-i-1,i-1) by i</a>, Intl. J. of Number Theory, 3, no.1 (2007), 119-139.
%o A178105 (Sage)
%o A178105 def A178105(n):
%o A178105     return next((d for d in (2..n//2) if binomial(n-d-1,d-1) % d == 0 and gcd(n,d) > 1), 0)
%o A178105 # _D. S. McNeil_, Sep 05 2011
%o A178105 (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
%Y A178105 Cf. A138389, A178071, A178098, A178099, A178100, A178101, A178109, A178110.
%K A178105 nonn
%O A178105 1,14
%A A178105 _Vladimir Shevelev_, May 20 2010
%E A178105 Corrected by _R. J. Mathar_, Sep 05 2011