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A046670 Partial sums of A006530. 8
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

K. Alladi and P. Erdos. “On an Additive Arithmetic Function.” Pacific J. Math. 71: 2 (1977), 275-294. MR 0447086 (56 #5401).

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

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.

Sequence in context: A190493 A070881 A046669 * A131383 A219730 A139001

Adjacent sequences:  A046667 A046668 A046669 * A046671 A046672 A046673

KEYWORD

nonn,nice,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from James A. Sellers

STATUS

approved

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Last modified February 25 03:06 EST 2018. Contains 299630 sequences. (Running on oeis4.)