A302752 Numbers k such that k divides the sum of largest parts of all partitions of k.

1, 3, 4, 5, 11, 197, 487, 928, 10995, 19318

Offset: 1

Author

Ilya Gutkovskiy, Apr 12 2018

Keywords

• nonn
• more

Comments

Numbers k such that k divides the total number of parts in all partitions of k.

Next term, if it exists, is greater than 100000. - Vaclav Kotesovec, May 04 2018

Examples

			5 is in the sequence because we have [5], [4, 1], [3, 2], [3, 1, 1], [2, 2, 1], [2, 1, 1, 1], [1, 1, 1, 1, 1] and 5 + 4 + 3 + 3 + 2 + 2 + 1 = 20 is divisible by 5.
		

Crossrefs

Cf. A006128, A051177.

Programs

Mathematica

Select[Range[200],Mod[Total[IntegerPartitions[#][[;;,1]]],#]==0&] (* The program generates the first six terms of the sequence. *) (* Harvey P. Dale, Oct 03 2023 *)