A316428 Heinz numbers of integer partitions such that every part is divisible by the number of parts.

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, 71, 73, 79, 83, 87, 89, 91, 97, 101, 103, 107, 109, 111, 113, 125, 127, 129, 131, 133, 137, 139, 149, 151, 157, 159, 163, 167, 169, 173, 179, 181, 183, 191, 193, 197

Offset: 1

Author

Gus Wiseman, Jul 02 2018

Keywords

• nonn

Comments

The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).

Examples

			93499 is the Heinz number of (12,8,8,4) and belongs to the sequence because each part is divisible by 4.
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).
		

Crossrefs

Cf. A056239, A067538, A074761, A143773, A237984, A289509, A296150, A298423, A316413.

Programs

Mathematica

Select[Range[200],And@@Cases[If[#==1,{},FactorInteger[#]],{p_,k_}:>Divisible[PrimePi[p],PrimeOmega[#]]]&]