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A112265 Cumulative sum of sum of initial digits of prime factors (with multiplicity) of n. 3
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 (list; graph; refs; listen; history; text; internal format)
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) = SUM{from i = 1 to n} A112264(i) = SUM{from i = 1 to 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 to A112273.

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

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Last modified September 26 05:09 EDT 2017. Contains 292502 sequences.