OFFSET
1,2
COMMENTS
Note that every i not exceeding n/2 for which (n,i)=1 divides binomial(n-i-1,i-1). For n>33, a(n) is either prime or square of a prime or a product of twin primes. For a proof, see link of V. Shevelev.
Numbers n such that A178105(n) = 0. - Michel Marcus, Feb 07 2016
LINKS
Peter J. C. Moses, Table of n, a(n) for n = 1..10000
V. Shevelev, On divisibility of binomial(n-i-1,i-1) by i, Intl. J. of Number Theory, 3, no.1 (2007), 119-139.
MATHEMATICA
Select[Range@ 200, Function[n, NoneTrue[Select[Range@ Floor[n/2], ! CoprimeQ[#, n] &], Divisible[Binomial[n - # - 1, # - 1], #] &]]] (* Michael De Vlieger, Feb 07 2016, Version 10 *)
PROG
(PARI) isok(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))); ); (md == -1); } \\ Michel Marcus, Feb 07 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, May 08 2008
STATUS
approved