A325619 Heinz numbers of integer partitions whose reciprocal factorial sum is 1.

2, 9, 375, 15625

Offset: 1

Author

Gus Wiseman, May 13 2019

Keywords

• nonn
• more

Comments

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

The reciprocal factorial sum of an integer partition (y_1,...,y_k) is 1/y_1! + ... + 1/y_k!.

Examples

			The sequence of terms together with their prime indices begins:
      1: {}
      2: {1}
      9: {2,2}
    375: {2,3,3,3}
  15625: {3,3,3,3,3,3}
		

Crossrefs

Factorial numbers: A000142, A007489, A022559, A064986, A108731, A115944, A284605, A325508, A325616.

Reciprocal factorial sum: A002966, A051908, A316855, A325618, A325624.

Programs

Mathematica

Select[Range[100000],Total[Cases[FactorInteger[#],{p_,k_}:>k/PrimePi[p]!]]==1&]

Formula

Contains prime(n)^(n!) for all n > 0, including 191581231380566414401 for n = 4.