A228562 Composite numbers k that are not prime powers such that binomial(2k-1, k-1) is congruent to 1 (mod k).

27173, 2001341, 16024189487

Offset

1,1

Links

Table of n, a(n) for n=1..3.

Richard J. McIntosh, On the converse of Wolstenholme's Theorem, Acta Arithmetica, 71 (1995), 381-389.

Formula

A099905(a(n)) = 1. - Jonathan Sondow, Jan 24 2016

Mathematica

Select[Range[30000], PrimeNu[#] > 1 && Mod[Binomial[2# - 1, # - 1], #] == 1 &] (* Alonso del Arte, May 11 2014 *)

Prog

(PARI) N=10^9; for(n=2, N, if(Mod(binomial(2*n-1, n-1), n)==1 && !ispower(n) && !isprime(n), print1(n, ", "))); \\ Felix Fröhlich, May 11 2014
(PARI) vp(n, p)=my(s); while(n\=p, s+=n); s
is(n)=my(f=factor(n)[, 1], G); if(#f==1, return(0)); for(i=1, #f, if(vp(2*n-1, f[i]) > vp(n, f[i])+vp(n-1, f[i]), return(0))); G=prod(i=1, #f, f[i]^(log(n)\log(f[i]))); prod(i=n+1, 2*n-1, i/gcd(i, G), Mod(1, n))/prod(i=2, n-1, i/gcd(i, G), Mod(1, n))==1
forcomposite(n=4, 1e9, if(is(n), print1(n", "))) \\ Charles R Greathouse IV, May 12 2014

Crossrefs

The odd terms of A328497.

Cf. A099905, A136327.

Sequence in context: A186481 A210073 A236275 * A224466 A127411 A268358

Adjacent sequences: A228559 A228560 A228561 * A228563 A228564 A228565

Keyword

hard,nonn,more,bref

Author

Felix Fröhlich, Aug 25 2013

Status

approved