A046669 Partial sums of A020639.

1, 3, 6, 8, 13, 15, 22, 24, 27, 29, 40, 42, 55, 57, 60, 62, 79, 81, 100, 102, 105, 107, 130, 132, 137, 139, 142, 144, 173, 175, 206, 208, 211, 213, 218, 220, 257, 259, 262, 264, 305, 307, 350, 352, 355, 357, 404, 406, 413, 415, 418, 420, 473

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• easy

References

• M. Kalecki, On certain sums extended over primes or prime factors (in Polish), Prace Mat., Vol. 8 (1963/64), pp. 121-129.
• József Sándor, Dragoslav S. Mitrinovic and Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, Section IV.1, p. 121.

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]

Crossrefs

Cf. A020639, A046670, A072486, A088821.

Programs

Haskell

a046669 n = a046669_list !! (n-1)
A046669_list = scanl1 (+) a020639_list -- Reinhard Zumkeller, Jun 15 2013

Mathematica

Accumulate[Array[FactorInteger[#][[1,1]]&,60]]  (* Harvey P. Dale, Apr 20 2011 *)

Formula

a(n) = A088821(n) + 1.

From Amiram Eldar, Mar 04 2021: (Start)

a(n) ~ ((1 + o(1))/2)* n^2/log(n) (Kalecki, 1963/64).

a(n) = (1/2) * n^2/log(n) + O(n^2/log(n)^2) (Brouwer, 1974). (End)