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A046670 Partial sums of A006530. 8


%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 K. Alladi and P. Erdos. “On an Additive Arithmetic Function.” Pacific J. Math. 71: 2 (1977), 275-294. MR 0447086 (56 #5401).

%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 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_

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Last modified December 12 15:01 EST 2017. Contains 295939 sequences.