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

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• easy

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]

Crossrefs

Cf. A006530, A046669, A104350, A360559.

Programs

Haskell

a046670 n = a046670_list !! (n-1)
a046670_list = scanl1 (+) a006530_list -- Reinhard Zumkeller, Jun 15 2013

Mathematica

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

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

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

Extensions

More terms from James Sellers