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

 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 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A168013 a(n) = Sum of all divisors of all numbers < (n+1)^2. 4
 8, 56, 189, 491, 1007, 1930, 3276, 5314, 8082, 11973, 16783, 23355, 31314, 41380, 53566, 68510, 85771, 106981, 130973, 159470, 192020, 229762, 271873, 320779, 375031, 436311, 504464, 581422, 664364, 759025, 860907, 973989, 1097783 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Partial sums of A168012. LINKS Chai Wah Wu, Table of n, a(n) for n = 1..10000 EXAMPLE For n=2 the a(2)=56 because the numbers < (2+1)^2 are 1,2,3,4,5,6,7 and 8. Then a(2)= sigma(1))+sigma(2)+sigma(3)+sigma(4)+sigma(5)+sigma(6)+sigma(7)+sigma(8) = 1+3+4+7+6+12+8+15 = 56, where sigma(n) is the sum of divisor of n (see A000203). MATHEMATICA A168012[n_]:=Sum[DivisorSigma[1, k], {k, n^2, (n+1)^2-1}]; Accumulate[Array[A168012, 50]] (* Paolo Xausa, Oct 23 2023 *) PROG (Python) def A168013(n): m = n*(n+2) return sum((q:=m//k)*((k<<1)+q+1) for k in range(1, n+1))-n**2*(n+1)>>1 # Chai Wah Wu, Oct 23 2023 CROSSREFS Cf. A000203, A024916, A168010, A168011, A168012. Sequence in context: A355948 A267522 A073831 * A003210 A135417 A248332 Adjacent sequences: A168010 A168011 A168012 * A168014 A168015 A168016 KEYWORD nonn AUTHOR Omar E. Pol, Nov 16 2009 EXTENSIONS More terms from Sean A. Irvine, Dec 07 2009 STATUS approved

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.

Last modified December 4 22:39 EST 2023. Contains 367565 sequences. (Running on oeis4.)