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 A073705 a(n) = Sum_{ d divides n } (n/d)^(2d). 7
 1, 5, 10, 33, 26, 182, 50, 577, 811, 1750, 122, 16194, 170, 18982, 74900, 135425, 290, 847127, 362, 2498178, 4901060, 4209430, 530, 78564226, 9766251, 67138102, 387952660, 542674914, 842, 4866184552, 962, 8606778369, 31382832260, 17179953862, 6385992100, 422091411267, 1370, 274878038710 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) is the number of linear partitions of the linearly ordered set [n] = {1,2,...,n} with blocks of the same size, where each block has two element marked (possibly equal). For instance, for n = 3, we have the following 10 linear partitions (where the marked elements are denoted by a and b, or by X when they coincide): (X)(X)(X), (ab3), (a2b), (1ab), (ba3), (b2a), (1ba), (X23), (1X3), (12X). - Emanuele Munarini, Feb 03 2014 LINKS Seiichi Manyama, Table of n, a(n) for n = 1..3143 FORMULA G.f.: Sum_{n>=1} -log(1 - (n^2)*x^n)/n = Sum_{n>=1} a(n) x^n/n. G.f.: Sum_{k>=1} k^2*x^k/(1-k^2*x^k). - Benoit Cloitre, Apr 21 2003 EXAMPLE a(10) = (10/1)^(2*1) +(10/2)^(2*2) +(10/5)^(2*5) +(10/10)^(2*10) = 1750 because positive divisors of 10 are 1, 2, 5, 10. MATHEMATICA Table[Total[Quotient[n, x = Divisors[n]]^(2*x)], {n, 34}] (* Jayanta Basu, Jul 08 2013 *) PROG (PARI) a(n)=sumdiv(n, d, (d)^(2*n/d) );  /* Joerg Arndt, Oct 07 2012 */ (Maxima) a(n):= lsum(d^(2*n/d), d, listify(divisors(n))); makelist(a(n), n, 1, 40); /* Emanuele Munarini , Feb 03 2014 */ CROSSREFS Cf. A038041, A055225, A151954, A236696. Sequence in context: A052538 A240413 A304215 * A328130 A121158 A214650 Adjacent sequences:  A073702 A073703 A073704 * A073706 A073707 A073708 KEYWORD easy,nonn AUTHOR Paul D. Hanna, Aug 04 2002 EXTENSIONS Corrected a(14) and inserted missing a(16) by Jayanta Basu, Jul 08 2013 STATUS approved

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Last modified November 14 09:43 EST 2019. Contains 329111 sequences. (Running on oeis4.)