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%I #4 Mar 30 2012 17:22:50
%S 2,4,6,8,9,12,13,14,17,18,20,22,23,26,25,29,30,32,33,36,37,37,41,42,
%T 44,45,45,51,49,53,54,53,58,57,62,62,65,63,66,70,70,72,73,74,78,77,79,
%U 84,81,86,85,90,87,93,93,94,97,99,99,100,102,105,105,109,109,109,115,111
%N The number of distinct prime factors occurring in the numbers between n^2 and (n+1)^2.
%C Same as the number of distinct prime factors in (2n^2+2n)!/(n^2)!. The plot appears nearly linear.
%H T. D. Noe, <a href="/A143346/b143346.txt">Table of n, a(n) for n=1..10000</a>
%e The numbers between 4 and 9 have factorizations 5, 2*3, 7, 2^4, which use primes 2, 3, 5 and 7. Hence a(2)=4.
%t Table[a=n^2; b=a+2*n; Sum[Sign[Quotient[b,p]-Quotient[a,p]], {p,Prime[Range[PrimePi[b]]]}], {n,100}]
%Y Cf. A014085 (number of primes between n^2 and (n+1)^2).
%K nonn
%O 1,1
%A _T. D. Noe_, Aug 09 2008
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