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%I #18 Feb 06 2018 12:09:55
%S 0,1,2,5,7,9,14,17,20,23,32,31,43,41,45,53,67,57,80,71,80,87,108,91,
%T 116,113,122,121,155,121,172,153,164,171,183,165,225,203,211,201,261,
%U 205,280,241,245,271,318,253,324,287,317,309,379,305,363,335,374
%N a(n) = Sum_{i=1..floor(n/2)} d( i*(n-i) ), where d(n) = the number of divisors of n.
%C For each partition of n into 2 parts, multiply the parts together and find the number of divisors of each product formed. Then add the results to get a(n).
%H Muniru A Asiru, <a href="/A253275/b253275.txt">Table of n, a(n) for n = 1..5000</a>
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F a(n) = Sum_{i=1..A004526(n)} A000005( i*(n-i) ).
%p with(numtheory): A253275:=n->add(tau(i*(n-i)), i=1..floor(n/2)): seq(A253275(n), n=1..100);
%t Table[Sum[DivisorSigma[0, i (n - i)], {i, 1, Floor[n/2]}], {n, 100}]
%o (PARI) a(n) = sum(i=1, n\2, numdiv(i*(n-i))); \\ _Michel Marcus_, Mar 18 2016
%o (GAP) List([1..10^4], n->Sum([1..Int(n/2)], i->Tau(i*(n-i)))); # _Muniru A Asiru_, Feb 04 2018
%Y Cf. A000005.
%K nonn,easy
%O 1,3
%A _Wesley Ivan Hurt_, May 01 2015