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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 (list; graph; refs; listen; history; text; internal format)
 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!. LINKS 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 Factorial numbers: A000142, A007489, A022559, A064986, A108731, A115944, A284605, A325508, A325616. Reciprocal factorial sum: A002966, A051908, A058360, A316854, A316857, A325619, A325621, A325622. Sequence in context: A090332 A325395 A070566 * A136327 A095415 A326149 Adjacent sequences:  A325620 A325621 A325622 * A325624 A325625 A325626 KEYWORD nonn AUTHOR Gus Wiseman, May 13 2019 STATUS approved

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Last modified April 17 02:26 EDT 2021. Contains 343059 sequences. (Running on oeis4.)