A325337 Numbers whose prime exponents are distinct and cover an initial interval of positive integers.

1, 2, 3, 5, 7, 11, 12, 13, 17, 18, 19, 20, 23, 28, 29, 31, 37, 41, 43, 44, 45, 47, 50, 52, 53, 59, 61, 63, 67, 68, 71, 73, 75, 76, 79, 83, 89, 92, 97, 98, 99, 101, 103, 107, 109, 113, 116, 117, 124, 127, 131, 137, 139, 147, 148, 149, 151, 153, 157, 163, 164

Offset

1,2

Comments

The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), so these are Heinz numbers of integer partitions with distinct multiplicities covering an initial interval of positive integers. The enumeration of these partitions by sum is given by A320348.

Links

Table of n, a(n) for n=1..61.

Example

The sequence of terms together with their prime indices begins:
   1: {}
   2: {1}
   3: {2}
   5: {3}
   7: {4}
  11: {5}
  12: {1,1,2}
  13: {6}
  17: {7}
  18: {1,2,2}
  19: {8}
  20: {1,1,3}
  23: {9}
  28: {1,1,4}
  29: {10}
  31: {11}
  37: {12}
  41: {13}
  43: {14}
  44: {1,1,5}

Mathematica

normQ[m_]:=Or[m=={}, Union[m]==Range[Max[m]]];
Select[Range[100], UnsameQ@@Last/@FactorInteger[#]&&normQ[Last/@FactorInteger[#]]&]

Crossrefs

Cf. A055932, A056239, A112798, A317081, A317089, A317090, A325326, A325330, A325370, A325371.

Sequence in context: A212166 A293511 A336615 * A342119 A372742 A324515

Adjacent sequences: A325334 A325335 A325336 * A325338 A325339 A325340

Keyword

nonn

Author

Gus Wiseman, May 01 2019

Status

approved