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%I #9 Feb 02 2016 12:14:34
%S 1,1,1,3,1,1,3,1,1,1,4,2,1,1,1,4,2,1,1,1,1,7,2,2,1,1,1,1,7,4,2,1,1,1,
%T 1,1,8,4,2,1,1,1,1,1,1,8,4,2,1,1,1,1,1,1,1,10,5,2,1,1,1,1,1,1,1,1,10,
%U 5,2,1,1,1,1,1,1,1,1,1,11,5,2,1,1,1,1,1,1,1,1,1,1,11,6,2,1,1,1,1,1,1,1,1,1
%N Triangle of T(n,k) = [n/k] + [n/k^2] + [n/k^3] + [n/k^4] + ... for n, k > 1.
%H Wenguang Zhai, <a href="http://dx.doi.org/10.1016/j.jnt.2009.02.016">On the prime power factorization of n!</a>, Journal of Number Theory, Volume 129, Issue 8, August 2009, Pages 1820-1836.
%F For p prime, T(n, p) = A090622(n, p) is the number of times that p is a factor of n!.
%e Rows start:
%e 1;
%e 1,1;
%e 3,1,1;
%e 3,1,1,1;
%e 4,2,1,1,1;
%e 4,2,1,1,1,1;
%e 7,2,2,1,1,1,1;
%e 7,4,2,1,1,1,1,1;
%e 8,4,2,1,1,1,1,1,1;
%e etc.
%o (PARI) t(n,k) = {my(s = 0, j = 1); while(p=n\k^j, s += p; j++); s;} \\ _Michel Marcus_, Feb 02 2016
%Y Rows include A011371, A054861, A054893, A027868, A054895, A054896, A054897, A054898, A054899, A064458, A064459, A090620, A054900.
%K nonn,tabl
%O 2,4
%A _Henry Bottomley_, Dec 06 2003
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