A330857 Total sum of divisors of all the parts in the partitions of n into 2 distinct parts.

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

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((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).

a(n) = A024916(n-1) for odd n >= 3, a(n) = A024916(n-1) - A000203(n/2) for even n. - Amiram Eldar, Dec 27 2024

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, A024916, A330856 (not necessarily distinct).

Sequence in context: A321348 A257311 A369790 * A066516 A047184 A002509

Adjacent sequences: A330854 A330855 A330856 * A330858 A330859 A330860

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Apr 27 2020

Status

approved