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%I #8 Apr 28 2020 00:27:45
%S 0,0,4,5,15,17,33,34,56,63,87,87,127,133,165,174,220,225,277,279,339,
%T 359,407,403,491,508,564,580,660,666,762,763,857,887,959,968,1098,
%U 1116,1196,1210,1342,1352,1480,1488,1608,1662,1758,1746,1930,1956,2080,2110,2250,2264
%N Total sum of divisors of all the parts in the partitions of n into 2 distinct parts.
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F a(n) = Sum_{i=1..floor((n-1)/2)} sigma(i) + sigma(n-i), where sigma(n) is the sum of divisors of n (A000203).
%F a(n) = - ((n+1) mod 2) * sigma(floor(n/2)) + Sum_{i=1..n-1} sigma(i), where sigma(n) is the sum of divisors of n (A000203).
%e a(6) = 17; 6 has two partitions into distinct parts, (5,1) and (4,2). The total sum of divisors of all the parts is then sigma(5) + sigma(1) + sigma(4) + sigma(2) = 6 + 1 + 7 + 3 = 17.
%t Table[Sum[DivisorSigma[1, i] + DivisorSigma[1, n - i], {i, Floor[(n - 1)/2]}], {n, 80}]
%Y Cf. A000203, A330856 (not necessarily distinct).
%K nonn,easy
%O 1,3
%A _Wesley Ivan Hurt_, Apr 27 2020
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