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A330857
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Total sum of divisors of all the parts in the partitions of n into 2 distinct parts.
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1
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0, 0, 4, 5, 15, 17, 33, 34, 56, 63, 87, 87, 127, 133, 165, 174, 220, 225, 277, 279, 339, 359, 407, 403, 491, 508, 564, 580, 660, 666, 762, 763, 857, 887, 959, 968, 1098, 1116, 1196, 1210, 1342, 1352, 1480, 1488, 1608, 1662, 1758, 1746, 1930, 1956, 2080, 2110, 2250, 2264
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OFFSET
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1,3
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LINKS
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FORMULA
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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).
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).
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EXAMPLE
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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.
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MATHEMATICA
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Table[Sum[DivisorSigma[1, i] + DivisorSigma[1, n - i], {i, Floor[(n - 1)/2]}], {n, 80}]
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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