A046670 - OEIS

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A046670

Partial sums of A006530.

1, 3, 6, 8, 13, 16, 23, 25, 28, 33, 44, 47, 60, 67, 72, 74, 91, 94, 113, 118, 125, 136, 159, 162, 167, 180, 183, 190, 219, 224, 255, 257, 268, 285, 292, 295, 332, 351, 364, 369, 410, 417, 460, 471, 476, 499, 546, 549, 556, 561, 578, 591, 644, 647, 658, 665, 684

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

REFERENCES

Handbook of Number Theory, D. S. Mitrinovic et al., Kluwer, Section IV.1.

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

K. Alladi and P. Erdős, On an additive arithmetic function, Pacific J. Math., Volume 71, Number 2 (1977), 275-294. MR 0447086 (56 #5401).

A. E. Brouwer, Two number theoretic sums, Stichting Mathematisch Centrum. Zuivere Wiskunde, Report ZW 19/74 (1974): 3 pages. [Cached copy, included with the permission of the author]

FORMULA

a(n) = Pi^2/12 * n^2/log n + O(n^2/log^2 n). [See Mitrinovic et al.] - Charles R Greathouse IV, Feb 19 2014

MATHEMATICA

Accumulate[Prepend[Table[FactorInteger[n][[-1, 1]], {n, 2, 100}], 1]] (* Harvey P. Dale, Jun 11 2011 *)

PROG

(Haskell)

a046670 n = a046670_list !! (n-1)

a046670_list = scanl1 (+) a006530_list -- Reinhard Zumkeller, Jun 15 2013

(PARI) gpf(n)=if(n<4, n, n=factor(n)[, 1]; n[#n])

a(n)=sum(k=1, n, gpf(k)) \\ Charles R Greathouse IV, Feb 19 2014

CROSSREFS

Cf. A046669, A104350.