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A325621
Heinz numbers of integer partitions whose reciprocal factorial sum is an integer.
5
1, 2, 4, 8, 9, 16, 18, 32, 36, 64, 72, 81, 128, 144, 162, 256, 288, 324, 375, 512, 576, 648, 729, 750, 1024, 1152, 1296, 1458, 1500, 2048, 2304, 2592, 2916, 3000, 3375, 4096, 4608, 5184, 5832, 6000, 6561, 6750, 8192, 9216, 10368, 11664, 12000, 13122, 13500
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}
4: {1,1}
8: {1,1,1}
9: {2,2}
16: {1,1,1,1}
18: {1,2,2}
32: {1,1,1,1,1}
36: {1,1,2,2}
64: {1,1,1,1,1,1}
72: {1,1,1,2,2}
81: {2,2,2,2}
128: {1,1,1,1,1,1,1}
144: {1,1,1,1,2,2}
162: {1,2,2,2,2}
256: {1,1,1,1,1,1,1,1}
288: {1,1,1,1,1,2,2}
324: {1,1,2,2,2,2}
375: {2,3,3,3}
512: {1,1,1,1,1,1,1,1,1}
MATHEMATICA
Select[Range[1000], IntegerQ[Total[Cases[FactorInteger[#], {p_, k_}:>k/PrimePi[p]!]]]&]
CROSSREFS
Reciprocal factorial sum: A002966, A058360, A316856, A325619, A325620, A325623.
Sequence in context: A152111 A316856 A324524 * A025611 A049439 A251642
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 13 2019
STATUS
approved