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A080084 Number of prime factors in the factorial of the n-th prime, counted with multiplicity.

%I A080084 #13 Jul 05 2019 16:58:33
%S A080084 1,2,5,8,16,20,29,33,41,56,60,76,85,89,98,114,129,134,151,160,166,180,
%T A080084 192,207,229,240,244,254,260,271,308,321,338,342,369,374,391,409,418,
%U A080084 435,451,457,484,492,502,507,541,572,585,590,601,616,623,653,674,689
%N A080084 Number of prime factors in the factorial of the n-th prime, counted with multiplicity.
%H A080084 Alois P. Heinz, <a href="/A080084/b080084.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Harvey P. Dale)
%F A080084 a(n) = Sum_{m=1..n} Sum_{k=1..L} floor( p_n /(p_m)^k ), where L = ceiling( log(p_n)/log(p_m) ).
%p A080084 b:= proc(n) option remember; `if`(n=1, 0,
%p A080084       b(n-1)+numtheory[bigomega](n))
%p A080084     end:
%p A080084 a:= n-> b(ithprime(n)):
%p A080084 seq(a(n), n=1..60);  # _Alois P. Heinz_, Jul 05 2019
%t A080084 PrimeOmega[#!]&/@Prime[Range[60]] (* _Harvey P. Dale_, Nov 09 2011 *)
%Y A080084 Cf. A080085, A080086, A080087.
%K A080084 nonn
%O A080084 1,2
%A A080084 _Paul D. Hanna_, Jan 26 2003