A112265 Cumulative sum of sum of initial digits of prime factors (with multiplicity) of n.

0, 2, 5, 9, 14, 19, 26, 32, 38, 45, 46, 53, 54, 63, 71, 79, 80, 88, 89, 98, 108, 111, 113, 122, 132, 135, 144, 155, 157, 167, 170, 180, 184, 187, 199, 209, 212, 215, 219, 230, 234, 246, 250, 255, 266, 270, 274, 285, 299, 311, 315, 320, 325, 336, 342, 355, 359

Offset: 1

Author

Jonathan Vos Post, Aug 30 2005

Keywords

• base
• easy
• nonn

Comments

Primes in this sequence are A112266.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000030, A000040, A001221, A001222, A112264, A112266.

Programs

Mathematica

f[1] = 0; f[n_] := Plus @@ (#[[2]] First@IntegerDigits[#[[1]]] & /@ FactorInteger[n]); Accumulate@ Array[f, 90] (* Giovanni Resta, Jun 17 2016 *)

Formula

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).

Extensions

Corrected and edited by Giovanni Resta, Jun 17 2016