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

1,2

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..61.

Example

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}

Mathematica

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

Crossrefs

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

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

Sequence in context: A088607 A296243 A162699 * A368603 A173263 A285141

Adjacent sequences: A325126 A325127 A325128 * A325130 A325131 A325132

Keyword

nonn

Author

Gus Wiseman, Apr 01 2019

Status

approved