A325129 Heinz numbers of integer partitions into nonsquares (A087153).

1, 3, 5, 9, 11, 13, 15, 17, 19, 25, 27, 29, 31, 33, 37, 39, 41, 43, 45, 47, 51, 55, 57, 59, 61, 65, 67, 71, 73, 75, 79, 81, 83, 85, 87, 89, 93, 95, 99, 101, 103, 107, 109, 111, 113, 117, 121, 123, 125, 127, 129, 131, 135, 137, 139, 141, 143, 145, 149, 153, 155

Offset: 1

Author

Gus Wiseman, Apr 01 2019

Keywords

• nonn

Comments

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

Examples

			The sequence of terms together with their prime indices begins:
   1: {}
   3: {2}
   5: {3}
   9: {2,2}
  11: {5}
  13: {6}
  15: {2,3}
  17: {7}
  19: {8}
  25: {3,3}
  27: {2,2,2}
  29: {10}
  31: {11}
  33: {2,5}
  37: {12}
  39: {2,6}
  41: {13}
  43: {14}
  45: {2,2,3}
		

Crossrefs

Cf. A001156, A011757, A033461, A056239, A062457, A066328, A087153, A112798.

Cf. A324571, A324587, A324588, A325128, A325130.

Programs

Mathematica

Select[Range[100],!MemberQ[If[#==1,{},FactorInteger[#]],{p_,_}/;IntegerQ[Sqrt[PrimePi[p]]]]&]