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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 (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}       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 Factorial numbers: A000142, A007489, A022559, A064986, A108731, A115944, A284605, A325508, A325616. Reciprocal factorial sum: A002966, A058360, A316856, A325619, A325620, A325623. Sequence in context: A152111 A316856 A324524 * A025611 A049439 A251642 Adjacent sequences:  A325618 A325619 A325620 * A325622 A325623 A325624 KEYWORD nonn AUTHOR Gus Wiseman, May 13 2019 STATUS approved

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Last modified August 13 18:00 EDT 2022. Contains 356107 sequences. (Running on oeis4.)