Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #31 Apr 25 2019 03:31:00
%S 1,3,6,8,13,16,23,25,28,33,44,47,60,67,72,74,91,94,113,118,125,136,
%T 159,162,167,180,183,190,219,224,255,257,268,285,292,295,332,351,364,
%U 369,410,417,460,471,476,499,546,549,556,561,578,591,644,647,658,665,684
%N Partial sums of A006530.
%D Handbook of Number Theory, D. S. Mitrinovic et al., Kluwer, Section IV.1.
%H T. D. Noe, <a href="/A046670/b046670.txt">Table of n, a(n) for n = 1..1000</a>
%H K. Alladi and P. Erdős, <a href="http://projecteuclid.org/euclid.pjm/1102811427">On an additive arithmetic function</a>, Pacific J. Math., Volume 71, Number 2 (1977), 275-294. MR 0447086 (56 #5401).
%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) = Pi^2/12 * n^2/log n + O(n^2/log^2 n). [See Mitrinovic et al.] - _Charles R Greathouse IV_, Feb 19 2014
%t Accumulate[Prepend[Table[FactorInteger[n][[-1,1]],{n,2,100}],1]] (* _Harvey P. Dale_, Jun 11 2011 *)
%o (Haskell)
%o a046670 n = a046670_list !! (n-1)
%o a046670_list = scanl1 (+) a006530_list -- _Reinhard Zumkeller_, Jun 15 2013
%o (PARI) gpf(n)=if(n<4,n,n=factor(n)[,1];n[#n])
%o a(n)=sum(k=1,n,gpf(k)) \\ _Charles R Greathouse IV_, Feb 19 2014
%Y Cf. A046669, A104350.
%K nonn,nice,easy
%O 1,2
%A _N. J. A. Sloane_
%E More terms from _James A. Sellers_