A120254 - OEIS

%I #5 Dec 11 2015 21:48:22

%S 0,0,0,0,1,0,1,2,1,2,2,2,3,2,5,3,4,4,5,4,5,7,5,6,6,7,9,5,9,7,8,11,8,

%T 11,8,10,9,13,12,10,12,12,13,14,12,15,15,12,17,14,17,14,19,15,17,18,

%U 17,17,19,20

%N Number of independent nonempty subsets of integers in the interval [n^2+1, (n+1)^2-1] whose product is a square. Independence is over GF(2^m).

%e a(8) = 2 because 66*70*75*77*80 = 46200^2 and 65*72*75*78*80 = 46800^2 and the last square 65*66*70*72*77*78 = 360360^2 is formed by combining the first two and dropping doubled terms.

%o (PARI) A120254(n) = local(f, m, p); f=vecsort(vector(2*n, i, if(vecmax(factor(2*core(n^2+1+i-1),2*n)[,1])<=2*n, n^2+i,0)),0,4); f=vecsort(vector(sum(i=1,#f, f[i]>1), i, f[i])); p=primes(primepi(2*n))~; m=matrix(#p,#f, i, j, core(f[j])%p[i]==0); matrank(matsolvemod(m,2,0,1)[2]%2)

%Y Cf. A099500, A099501, A120253.

%K nonn

%O 1,8

%A _Martin Fuller_, Jun 13 2006