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

2, 9, 375, 15625

Offset

1,1

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!.

Links

Table of n, a(n) for n=1..4.

Formula

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

Example

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}

Mathematica

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

Crossrefs

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

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

Sequence in context: A013169 A012991 A003818 * A049299 A024225 A266289

Adjacent sequences: A325616 A325617 A325618 * A325620 A325621 A325622

Keyword

nonn,more

Author

Gus Wiseman, May 13 2019

Status

approved