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A298946 a(n) = binomial(2*c-1, c-1) (mod c^4), where c is the n-th composite number.

%I A298946 #14 Feb 03 2018 12:28:41
%S A298946 35,462,2339,4627,2378,4238,5148,1260,57635,85026,64410,100509,163716,
%T A298946 171918,93876,309780,148969,444220,370712,532771,652200,938386,816466,
%U A298946 907874,569300,1107298,2470810,2953692,887812,1341810,2956584,1941390,589961,6248628
%N A298946 a(n) = binomial(2*c-1, c-1) (mod c^4), where c is the n-th composite number.
%C A298946 Composites c where a(n) = 1 could be called "Wolstenholme pseudoprimes". Do any such composites exist?
%C A298946 A necessary condition for c to be a "Wolstenholme pseudoprime" would be that it is a term of A228562 or A267824.
%H A298946 Robert Israel, <a href="/A298946/b298946.txt">Table of n, a(n) for n = 1..10000</a>
%p A298946 R:= NULL:
%p A298946 count:= 0: F:= 10;
%p A298946 for n from 4 while count < 100 do
%p A298946   F:= F * (4*n-2)/n;
%p A298946   if not isprime(n) then
%p A298946      count:= count+1;
%p A298946      R:= R, F mod (n^4);
%p A298946   fi
%p A298946 od:
%p A298946 R; # _Robert Israel_, Feb 02 2018
%t A298946 Table[Mod[Binomial[2 c - 1, c - 1], c^4], {c, Select[Range@ 50, CompositeQ]}] (* _Michael De Vlieger_, Feb 01 2018 *)
%o A298946 (PARI) forcomposite(c=1, 200, print1(lift(Mod(binomial(2*c-1, c-1), c^4)), ", "))
%o A298946 (Python)
%o A298946 from sympy import binomial, composite
%o A298946 def A298946(n):
%o A298946     c = composite(n)
%o A298946     return binomial(2*c-1,c-1) % c**4 # _Chai Wah Wu_, Feb 02 2018
%Y A298946 Cf. A088164, A228562, A244214, A267824, A281302, A298944, A298945.
%K A298946 nonn
%O A298946 1,1
%A A298946 _Felix Fröhlich_, Jan 30 2018