A325259 Numbers with one fewer distinct prime exponents than distinct prime factors.

6, 10, 14, 15, 21, 22, 26, 33, 34, 35, 36, 38, 39, 46, 51, 55, 57, 58, 60, 62, 65, 69, 74, 77, 82, 84, 85, 86, 87, 90, 91, 93, 94, 95, 100, 106, 111, 115, 118, 119, 120, 122, 123, 126, 129, 132, 133, 134, 140, 141, 142, 143, 145, 146, 150, 155, 156, 158, 159

Offset

1,1

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 one fewer distinct multiplicities than distinct parts. The enumeration of these partitions by sum is given by A325244.

Links

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

Formula

A001221(a(n)) = A071625(a(n)) + 1.

Example

The sequence of terms together with their prime indices begins:
    6: {1,2}
   10: {1,3}
   14: {1,4}
   15: {2,3}
   21: {2,4}
   22: {1,5}
   26: {1,6}
   33: {2,5}
   34: {1,7}
   35: {3,4}
   36: {1,1,2,2}
   38: {1,8}
   39: {2,6}
   46: {1,9}
   51: {2,7}
   55: {3,5}
   57: {2,8}
   58: {1,10}
   60: {1,1,2,3}
   62: {1,11}

Mathematica

Select[Range[100], PrimeNu[#]==Length[Union[Last/@FactorInteger[#]]]+1&]

Crossrefs

Cf. A056239, A060687, A090858, A112798, A116608, A118914, A130091, A323023, A325241, A325242, A325244, A325270, A325281.

Sequence in context: A327829 A052053 A276818 * A320911 A371781 A362617

Adjacent sequences: A325256 A325257 A325258 * A325260 A325261 A325262

Keyword

nonn

Author

Gus Wiseman, Apr 18 2019

Status

approved