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A227314 Number of prime factors, with multiplicity, of the sum of the first n composite numbers.

%I A227314 #14 Oct 06 2024 09:14:34
%S A227314 2,2,3,3,1,2,3,3,2,5,4,3,3,1,6,4,1,2,2,1,6,3,2,2,2,3,2,4,4,2,2,3,8,3,
%T A227314 1,1,1,3,2,2,2,2,1,2,3,2,1,1,3,3,4,2,1,1,3,7,7,3,2,4,4,2,1,1,2,4,2,1,
%U A227314 3,4,4,3,1,1,1,2,5,2,3,6,2,2,3,6,5,1,5,3,2,3,2,6,7,2,2,2,6,3,2,3
%N A227314 Number of prime factors, with multiplicity, of the sum of the first n composite numbers.
%H A227314 Amiram Eldar, <a href="/A227314/b227314.txt">Table of n, a(n) for n = 1..10000</a>
%F A227314 a(n) = A001222(A053767(n)).
%e A227314 a(10) = 5 because A053767(10) = 4 + 6 + 8 + 9 + 10 + 12 + 14 + 15 + 16 + 18 = 112 = 2^4 * 7, which has 5 prime factors, with multiplicity.
%p A227314 A227314 := proc(n)
%p A227314     A001222(A053767(n)) ;
%p A227314 end proc: # _R. J. Mathar_, Jul 06 2013
%t A227314 PrimeOmega[Accumulate[Select[Range[150], CompositeQ]]] (* _Amiram Eldar_, Oct 06 2024 *)
%Y A227314 Cf. A001222, A002808, A053767.
%K A227314 nonn,easy
%O A227314 1,1
%A A227314 _Jonathan Vos Post_, Jul 06 2013