Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #9 Oct 03 2023 15:48:00
%S 1,3,4,5,11,197,487,928,10995,19318
%N Numbers k such that k divides the sum of largest parts of all partitions of k.
%C Numbers k such that k divides the total number of parts in all partitions of k.
%C Next term, if it exists, is greater than 100000. - _Vaclav Kotesovec_, May 04 2018
%e 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.
%t Select[Range[200],Mod[Total[IntegerPartitions[#][[;;,1]]],#]==0&] (* The program generates the first six terms of the sequence. *) (* _Harvey P. Dale_, Oct 03 2023 *)
%Y Cf. A006128, A051177.
%K nonn,more
%O 1,2
%A _Ilya Gutkovskiy_, Apr 12 2018