login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A072481 a(n) = Sum_{k=1..n} Sum_{d=1..k} (k mod d). 5

%I

%S 0,0,0,1,2,6,9,17,25,37,50,72,89,117,148,184,220,271,318,382,443,513,

%T 590,688,773,876,988,1113,1237,1388,1526,1693,1860,2044,2241,2459,

%U 2657,2890,3138,3407,3665,3962,4246,4571,4899,5238,5596,5999,6373,6787,7207

%N a(n) = Sum_{k=1..n} Sum_{d=1..k} (k mod d).

%C Previous name was: Sums of sums of remainders when dividing n by k, 0<k<=n.

%C Partial sums of A004125.

%H Robert Israel, <a href="/A072481/b072481.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = Sum_{k=1..n}Sum_{d=1..k}(k mod d).

%F a(n) = A000330(n) - A175254(n), n >= 1. - _Omar E. Pol_, Aug 12 2015

%F G.f.: x^2/(1-x)^4 - (1-x)^(-2) * Sum_{k>=1} k*x^(2*k)/(1-x^k). - _Robert Israel_, Aug 13 2015

%F a(n) ~ (1 - Pi^2/12)*n^3/3. - _Vaclav Kotesovec_, Sep 25 2016

%p N:= 200: # to get a(0) to a(N)

%p S:= series(add(k*x^(2*k)/(1-x^k),k=1..floor(N/2))/(1-x)^2, x, N+1):

%p seq((n^3-n)/6 - coeff(S,x,n), n=0..N); # _Robert Israel_, Aug 13 2015

%o (Python)

%o for n in range(99):

%o s = 0

%o for k in range(1,n+1):

%o for d in range(1,k+1):

%o s += k % d

%o print str(s)+',',

%o (PARI) a(n) = sum(k=1, n, sum(d=1, k, k % d)); \\ _Michel Marcus_, Feb 11 2014

%Y Cf. A224923, A224924.

%K nonn

%O 0,5

%A _Reinhard Zumkeller_, Aug 02 2002

%E New name and a(0) from _Alex Ratushnyak_, Feb 10 2014

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 22 05:30 EST 2018. Contains 317453 sequences. (Running on oeis4.)