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 A075833 Least k such that for any p prime dividing n, p does not divide binomial((n+1)*k,k+1) or 0 if no k was found. 0

%I

%S 1,1,2,3,4,11,6,7,8,29,10,0,12,55,29,15,16,0,18,259,62,131,22,71,24,

%T 519,26,55,28,0,30,31,32,305,34,0,36,0

%N Least k such that for any p prime dividing n, p does not divide binomial((n+1)*k,k+1) or 0 if no k was found.

%C It seems that if p is prime a(6p) doesn't exist.

%F It seems that if p is prime a(p^m)=p^m-1 m>0

%o (PARI) D(k,n)=binomial((n+1)*k,k+1); div(n)=divisors(n); a(n)=if(n<0,0,k=1; while(prod(i=1,numdiv(n),D(k,n)%if(isprime(component(div(n),i)), component(div(n),i),D(k,n)+1)) == 0,k++); k)

%K more,nonn

%O 1,3

%A _Benoit Cloitre_, Oct 14 2002

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Last modified June 17 17:12 EDT 2019. Contains 324196 sequences. (Running on oeis4.)