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 A007437 Inverse Moebius transform of triangular numbers. (Formerly M3309) 23
 1, 4, 7, 14, 16, 31, 29, 50, 52, 74, 67, 119, 92, 137, 142, 186, 154, 247, 191, 294, 266, 323, 277, 455, 341, 446, 430, 553, 436, 686, 497, 714, 634, 752, 674, 1001, 704, 935, 878, 1150, 862, 1298, 947, 1323, 1222, 1361, 1129, 1767, 1254, 1674, 1486, 1834 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Alois P. Heinz, Table of n, a(n) for n = 1..10000 M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version] M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures] N. J. A. Sloane, Transforms FORMULA Coefficients in expansion of Sum_{n >= 1} x^n/(1-x^n)^3. G.f.: sum(n>=1, (n*(n+1)/2) * x^n/(1-x^n) ). - Joerg Arndt, Jan 30 2011 a(n)=sum(d|n, d*(d+1)/2)= (1/2) *(sigma(n)+sigma_2(n))= (1/2) *(A000203(n)+A001157(n)). - Benoit Cloitre, Apr 08 2002 Row sums of triangles A134544 and A134545. - Gary W. Adamson, Oct 31 2007 Row sums of triangle A134839 - Gary W. Adamson, Nov 12 2007 Dirichlet g.f. zeta(s)*(zeta(s-1)+zeta(s-2))/2. [From Franklin T. Adams-Watters, Nov 05 2009] L.g.f.: -log(Product_{k>=1} (1 - x^k)^((k+1)/2)) = Sum_{n>=1} a(n)*x^n/n. - Ilya Gutkovskiy, Mar 12 2018 Sum_{k=1..n} a(k) ~ Zeta(3) * n^3 / 6. - Vaclav Kotesovec, Nov 06 2018 MAPLE with(numtheory): a:= proc(n) option remember;       add(d*(d+1)/2, d=divisors(n))     end: seq(a(n), n=1..60);  # Alois P. Heinz, Feb 09 2011 MATHEMATICA a[n_] := (DivisorSigma[1, n] + DivisorSigma[2, n])/2; Table[a[n], {n, 1, 60}] (* Jean-François Alcover, Mar 10 2014, after Benoit Cloitre *) PROG (PARI) a(n)=if(n<1, 1, sumdiv(n, d, (d^2+d))/2); /* Joerg Arndt, Aug 14 2012 */ CROSSREFS Cf. A134544, A134545. Cf. A134839, A301873, A301874. Sequence in context: A310897 A310898 A310899 * A310900 A310901 A310902 Adjacent sequences:  A007434 A007435 A007436 * A007438 A007439 A007440 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from Christian G. Bower. STATUS approved

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Last modified August 11 13:02 EDT 2020. Contains 336428 sequences. (Running on oeis4.)