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

1,2

Comments

Primes in this sequence are A112266.

Links

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

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).

Mathematica

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

Crossrefs

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

Sequence in context: A235333 A060139 A266899 * A025281 A160663 A024201

Adjacent sequences: A112262 A112263 A112264 * A112266 A112267 A112268

Keyword

base,easy,nonn

Author

Jonathan Vos Post, Aug 30 2005

Extensions

Corrected and edited by Giovanni Resta, Jun 17 2016

Status

approved