A352257 Sum of all parts of all partitions of n into an odd number of consecutive parts.

1, 2, 3, 4, 5, 12, 7, 8, 18, 10, 11, 24, 13, 14, 45, 16, 17, 36, 19, 40, 42, 22, 23, 48, 50, 26, 54, 56, 29, 90, 31, 32, 66, 34, 105, 72, 37, 38, 78, 80, 41, 126, 43, 44, 180, 46, 47, 96, 98, 100, 102, 52, 53, 162, 110, 112, 114, 58, 59, 180, 61, 62, 252, 64, 130, 198

Offset: 1

Author

Omar E. Pol, Mar 09 2022

Keywords

• nonn

Comments

a(n) is n times the number of partitions of n into an odd number of consecutive parts.

Examples

			For n = 15 the partitions of 15 into an odd number of consecutive parts are [15], [6, 5, 4] and [5, 4, 3, 2, 1], so a(15) = 15 + 6 + 5 + 4 + 5 + 4 + 3 + 2 + 1 = 15*3 = 45.
		

Crossrefs

Row sums of A352499.

Cf. A066186, A082647, A237048, A245579, A286000, A286001, A299765, A351824, A352505.

Programs

PARI

a(n) = my(q = sqrt(2*n)); n*sumdiv(n, d, (d%2) && (d < q)); \\ Michel Marcus, Mar 11 2022; after A082647

Formula

a(n) = n*A082647(n).

a(n) = A245579(n) - A352505(n). - Omar E. Pol, Mar 19 2022