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 A055507 Sum{k = 1 to n}[d(k)*d(n+1-k)], where d(k) is number of positive divisors of k. 11
 1, 4, 8, 14, 20, 28, 37, 44, 58, 64, 80, 86, 108, 108, 136, 134, 169, 160, 198, 192, 236, 216, 276, 246, 310, 288, 348, 310, 400, 344, 433, 396, 474, 408, 544, 450, 564, 512, 614, 522, 688, 560, 716, 638, 756, 636, 860, 676, 859, 772, 926, 758, 1016, 804, 1032 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) = number of ordered ways to express n+1 as a*b+c*d with 1 <= a,b,c,d <= n. - David W. Wilson, Jun 16 2003 tau(n) (A000005) convolved with itself, treating this result as a sequence whose offset is 2. - Graeme McRae, Jun 06 2006 REFERENCES Titchmarsh, E. C. "Some problems in the analytic theory of numbers." The Quarterly Journal of Mathematics 1 (1942): 129-152. LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 George E. Andrews, Stacked lattice boxes, Ann. Comb. 3 (1999), 115-130. See D_{0,0}. Yoichi Motohashi, The binary additive divisor problem, Annales scientifiques de l'École Normale Supérieure, Sér. 4, 27 no. 5 (1994), p. 529-572. FORMULA G.f.: Sum_{i >= 1, j >= 1} x^(i+j-1)/(1-x^i)/(1-x^j). - Vladeta Jovovic, Nov 11 2001 Working with an offset of 2, it appears that the o.g.f is equal to the Lambert series sum {n >= 2} A072031(n-1)*x^n/(1 - x^n). - Peter Bala, Dec 09 2014 EXAMPLE a = d(1)*d(4) + d(2)*d(3) + d(3)*d(2) + d(4)*d(1) = 1*3 +2*2 +2*2 +3*1 = 14 3 = 1*1+2*1 in 4 ways, so a(2)=4; 4 = 1*1+1*3 (4 ways) = 2*1+2*1 (4 ways), so a(3)=8; 5 = 4*1+1*1 (4 ways) = 2*2+1*1 (2 ways) + 3*1+2*1 (8 ways), so a(4) = 14. - N. J. A. Sloane, Jul 07 2012 MAPLE with(numtheory); D00:=n->add(tau(j)*tau(n-j), j=1..n-1); PROG (PARI) a(n)=sum(k=1, n, numdiv(k)*numdiv(n+1-k)) \\ Charles R Greathouse IV, Oct 17 2012 CROSSREFS Cf. A000385, A072031. Sequence in context: A317292 A276221 A265284 * A121896 A173290 A312686 Adjacent sequences:  A055504 A055505 A055506 * A055508 A055509 A055510 KEYWORD nonn AUTHOR Leroy Quet, Jun 29 2000 EXTENSIONS More terms from James A. Sellers, Jul 04 2000 Definition clarified by N. J. A. Sloane, Jul 07 2012 STATUS approved

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Last modified July 9 16:50 EDT 2020. Contains 335545 sequences. (Running on oeis4.)