A284475 Total number of parts in all partitions of n into equal parts, minus the total number of parts in all partitions of n into consecutive parts.

0, 2, 1, 6, 3, 8, 5, 14, 7, 13, 9, 24, 11, 19, 13, 30, 15, 31, 17, 36, 20, 31, 21, 56, 23, 37, 28, 48, 27, 59, 29, 62, 36, 49, 33, 79, 35, 55, 44, 84, 39, 81, 41, 75, 52, 67, 45, 120, 47, 83, 60, 89, 51, 103, 54, 112, 68, 85, 57, 151, 59, 91, 76, 126, 66, 125, 65, 117, 84, 127, 69, 182, 71, 109, 97, 131, 75, 148

Offset: 1

Author

Omar E. Pol, May 03 2017

Keywords

• nonn

Comments

Observation: at least for the first 78 terms of this sequence the values of n where a(n) = n - 2 coincide with the odd numbers of A082664.

Examples

			For n = 10 the partitions of 10 into equal parts are [10], [5, 5], [2, 2, 2, 2, 2] and [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]. The total number of parts is 18. On the other hand, the partitions of 10 into consecutive parts are [10] and [4, 3, 2, 1]. The total number of parts is 5, so a(10) = 18 - 5 = 13.
		

Crossrefs

Cf. A000203, A000918, A082647, A082664, A204217, A285914.

Formula

Conjecture: a(n) = A000203(n) - A204217(n).

a(2^k) = A000918(k+1), k>=0.