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%I #10 Jan 15 2015 16:22:11
%S 0,1,1,2,4,5,6,8,9,13,14,17,18,19,21,23,27,28,31,32,34,36,40,42,46,48,
%T 49,50,53,54,61,62,66,67,71,72,75,80,81,84,86,88,93,94,95,97,102,108,
%U 110,111,112,115,116,123,126,129,131,134,136,138,139,143,151,152,153
%N Number of factors of 3 in the factorial of the n-th prime, counted with multiplicity.
%F a(n) = sum_{k=1..L} floor(prime(n) / 3^k), where L = log(p_n)/log(3).
%t lst={};Do[p=Prime[n];s=0;While[p>1,p=IntegerPart[p/3];s+=p;];AppendTo[lst,s],{n,5!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Jul 28 2009 *)
%t Join[{0},FactorInteger[#][[2,2]]&/@(Prime[Range[2,70]]!)] (* _Harvey P. Dale_, Sep 05 2014 *)
%Y Cf. A080084, A080085, A080087.
%K nonn
%O 1,4
%A _Paul D. Hanna_, Jan 26 2003
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