A316428 - 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