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

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.

Sequence in context: A070881 A046669 A352773 * A131383 A219730 A337484

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