%I #32 Jan 05 2024 07:25:10
%S 1,3,6,8,13,15,22,24,27,29,40,42,55,57,60,62,79,81,100,102,105,107,
%T 130,132,137,139,142,144,173,175,206,208,211,213,218,220,257,259,262,
%U 264,305,307,350,352,355,357,404,406,413,415,418,420,473
%N Partial sums of A020639.
%D M. Kalecki, On certain sums extended over primes or prime factors (in Polish), Prace Mat., Vol. 8 (1963/64), pp. 121-129.
%D József Sándor, Dragoslav S. Mitrinovic and Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, Section IV.1, p. 121.
%H T. D. Noe, <a href="/A046669/b046669.txt">Table of n, a(n) for n = 1..1000</a>
%H A. E. Brouwer, <a href="/A046670/a046670.pdf">Two number theoretic sums</a>, Stichting Mathematisch Centrum. Zuivere Wiskunde, Report ZW 19/74 (1974): 3 pages. [Cached copy, included with the permission of the author]
%F a(n) = A088821(n) + 1.
%F From _Amiram Eldar_, Mar 04 2021: (Start)
%F a(n) ~ ((1 + o(1))/2)* n^2/log(n) (Kalecki, 1963/64).
%F a(n) = (1/2) * n^2/log(n) + O(n^2/log(n)^2) (Brouwer, 1974). (End)
%t Accumulate[Array[FactorInteger[#][[1,1]]&,60]] (* _Harvey P. Dale_, Apr 20 2011 *)
%o (Haskell)
%o a046669 n = a046669_list !! (n-1)
%o A046669_list = scanl1 (+) a020639_list -- _Reinhard Zumkeller_, Jun 15 2013
%Y Cf. A020639, A046670, A072486, A088821.
%K nonn,nice,easy
%O 1,2
%A _N. J. A. Sloane_