A316520 Heinz numbers of integer partitions whose average is a prime number.

3, 5, 9, 10, 11, 17, 21, 22, 25, 27, 28, 30, 31, 41, 46, 57, 59, 67, 68, 78, 81, 82, 83, 84, 85, 88, 90, 91, 98, 99, 100, 105, 109, 110, 111, 121, 125, 127, 146, 155, 157, 164, 179, 184, 191, 194, 203, 208, 211, 213, 222, 228, 241, 243, 247, 252, 253, 264, 267

Offset: 1

Author

Gus Wiseman, Jul 05 2018

Keywords

• nonn

Comments

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

Examples

			60 = 2*2*3*5 has prime indices {1,1,2,3} with average 7/4, so 60 does not belong to the sequence.
90 = 2*3*3*5 has prime indices {1,2,2,3} with average 8/2 = 4, so 90 belongs to the sequence.
		

Crossrefs

Cf. A000040, A000041, A000607, A056239, A067538, A078175, A100118, A237984, A296150, A316313, A316413.

Programs

Mathematica

Select[Range[100],PrimeQ[Mean[If[#==1,{},Flatten[Cases[FactorInteger[#],{p_,k_}:>Table[PrimePi[p],{k}]]]]]]&]