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%I #20 Nov 03 2023 12:00:05
%S 0,2,5,9,14,19,26,32,38,45,46,53,54,63,71,79,80,88,89,98,108,111,113,
%T 122,132,135,144,155,157,167,170,180,184,187,199,209,212,215,219,230,
%U 234,246,250,255,266,270,274,285,299,311,315,320,325,336,342,355,359
%N Cumulative sum of sum of initial digits of prime factors (with multiplicity) of n.
%C Primes in this sequence are A112266.
%H G. C. Greubel, <a href="/A112265/b112265.txt">Table of n, a(n) for n = 1..1000</a>
%F a(1) = 0 and given the prime factorization i = (p_1)^(e_1) * (p_2)^(e_2) * ... * (p_k)^(e_k) then a(n) = Sim_{i=1..n} A112264(i) = Sum_{i=1..n} (e_1)*A000030(p_1) + (e_2)*A000030(p_2) + ... + (e_k)*A000030(p_l).
%t f[1] = 0; f[n_] := Plus @@ (#[[2]] First@IntegerDigits[#[[1]]] & /@ FactorInteger[n]); Accumulate@ Array[f, 90] (* _Giovanni Resta_, Jun 17 2016 *)
%Y Cf. A000030, A000040, A001221, A001222, A112264, A112266.
%K base,easy,nonn
%O 1,2
%A _Jonathan Vos Post_, Aug 30 2005
%E Corrected and edited by _Giovanni Resta_, Jun 17 2016
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