|
| |
|
|
A325619
|
|
Heinz numbers of integer partitions whose reciprocal factorial sum is 1.
|
|
7
|
| |
|
|
|
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
|
| |
|
|
