login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A046669 Partial sums of A020639. 5

%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_

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)