

A330857


Total sum of divisors of all the parts in the partitions of n into 2 distinct parts.


1



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

1,3


LINKS

Table of n, a(n) for n=1..54.
Index entries for sequences related to partitions


FORMULA

a(n) = Sum_{i=1..floor((n1)/2)} sigma(i) + sigma(ni), where sigma(n) is the sum of divisors of n (A000203).
a(n) =  ((n+1) mod 2) * sigma(floor(n/2)) + Sum_{i=1..n1} sigma(i), where sigma(n) is the sum of divisors of n (A000203).


EXAMPLE

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.


MATHEMATICA

Table[Sum[DivisorSigma[1, i] + DivisorSigma[1, n  i], {i, Floor[(n  1)/2]}], {n, 80}]


CROSSREFS

Cf. A000203, A330856 (not necessarily distinct).
Sequence in context: A308095 A321348 A257311 * A066516 A047184 A002509
Adjacent sequences: A330854 A330855 A330856 * A330858 A330859 A330860


KEYWORD

nonn,easy


AUTHOR

Wesley Ivan Hurt, Apr 27 2020


STATUS

approved



