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A325623
Heinz numbers of integer partitions whose reciprocal factorial sum is the reciprocal of an integer.
6
1, 2, 3, 5, 7, 9, 11, 13, 17, 19, 23, 25, 29, 31, 37, 41, 43, 47, 49, 53, 59, 61, 67, 71, 73, 77, 79, 83, 89, 97, 101, 103, 107, 109, 113, 121, 125, 127, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 211, 221, 223, 227, 229
OFFSET
1,2
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!.
EXAMPLE
The sequence of terms together with their prime indices begins:
1: {}
2: {1}
3: {2}
5: {3}
7: {4}
9: {2,2}
11: {5}
13: {6}
17: {7}
19: {8}
23: {9}
25: {3,3}
29: {10}
31: {11}
37: {12}
41: {13}
43: {14}
47: {15}
49: {4,4}
53: {16}
MATHEMATICA
Select[Range[100], IntegerQ[1/Total[Cases[FactorInteger[#], {p_, k_}:>k/PrimePi[p]!]]]&]
CROSSREFS
Reciprocal factorial sum: A002966, A051908, A058360, A316854, A316857, A325619, A325621, A325622.
Sequence in context: A090332 A325395 A070566 * A136327 A095415 A326149
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 13 2019
STATUS
approved