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%I #29 Nov 05 2017 07:44:37
%S 1,5,10,33,26,182,50,577,811,1750,122,16194,170,18982,74900,135425,
%T 290,847127,362,2498178,4901060,4209430,530,78564226,9766251,67138102,
%U 387952660,542674914,842,4866184552,962,8606778369,31382832260,17179953862,6385992100,422091411267,1370,274878038710
%N a(n) = Sum_{ d divides n } (n/d)^(2d).
%C 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):
%C (X)(X)(X), (ab3), (a2b), (1ab), (ba3), (b2a), (1ba), (X23), (1X3), (12X). - _Emanuele Munarini_, Feb 03 2014
%H Seiichi Manyama, <a href="/A073705/b073705.txt">Table of n, a(n) for n = 1..3143</a>
%F G.f.: Sum_{n>=1} -log(1 - (n^2)*x^n)/n = Sum_{n>=1} a(n) x^n/n.
%F G.f.: Sum_{k>=1} k^2*x^k/(1-k^2*x^k). - _Benoit Cloitre_, Apr 21 2003
%e 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.
%t Table[Total[Quotient[n, x = Divisors[n]]^(2*x)], {n, 34}] (* _Jayanta Basu_, Jul 08 2013 *)
%o (PARI) a(n)=sumdiv(n, d, (d)^(2*n/d) ); /* _Joerg Arndt_, Oct 07 2012 */
%o (Maxima) a(n):= lsum(d^(2*n/d),d,listify(divisors(n)));
%o makelist(a(n),n,1,40); /* _Emanuele Munarini_ , Feb 03 2014 */
%Y Cf. A038041, A055225, A151954, A236696.
%K easy,nonn
%O 1,2
%A _Paul D. Hanna_, Aug 04 2002
%E Corrected a(14) and inserted missing a(16) by _Jayanta Basu_, Jul 08 2013
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