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 #5 Jul 03 2018 07:29:03
%S 1,2,3,5,7,9,11,13,17,19,21,23,29,31,37,39,41,43,47,49,53,57,59,61,67,
%T 71,73,79,83,87,89,91,97,101,103,107,109,111,113,125,127,129,131,133,
%U 137,139,149,151,157,159,163,167,169,173,179,181,183,191,193,197
%N Heinz numbers of integer partitions such that every part is divisible by the number of parts.
%C The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%e 93499 is the Heinz number of (12,8,8,4) and belongs to the sequence because each part is divisible by 4.
%e Sequence of partitions such that every part is divisible by the number of parts begins (1), (2), (3), (4), (2,2), (5), (6), (7), (8), (4,2), (9).
%t Select[Range[200],And@@Cases[If[#==1,{},FactorInteger[#]],{p_,k_}:>Divisible[PrimePi[p],PrimeOmega[#]]]&]
%Y Cf. A056239, A067538, A074761, A143773, A237984, A289509, A296150, A298423, A316413.
%K nonn
%O 1,2
%A _Gus Wiseman_, Jul 02 2018