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

1,1

Comments

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

Links

Table of n, a(n) for n=1..59.

Example

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.

Mathematica

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

Crossrefs

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

Sequence in context: A081500 A338655 A030365 * A153710 A230385 A269399

Adjacent sequences: A316517 A316518 A316519 * A316521 A316522 A316523

Keyword

nonn

Author

Gus Wiseman, Jul 05 2018

Status

approved