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A325619
Heinz numbers of integer partitions whose reciprocal factorial sum is 1.
7
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!.
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
Reciprocal factorial sum: A002966, A051908, A316855, A325618, A325624.
Sequence in context: A013169 A012991 A003818 * A049299 A024225 A266289
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, May 13 2019
STATUS
approved