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

1,2

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]

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)

Mathematica

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

Prog

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

Crossrefs

Cf. A020639, A046670, A072486, A088821.

Sequence in context: A084578 A190493 A070881 * A352773 A046670 A131383

Adjacent sequences: A046666 A046667 A046668 * A046670 A046671 A046672

Keyword

nonn,nice,easy

Author

N. J. A. Sloane

Status

approved