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 A307895 Numbers whose prime exponents, starting from the largest prime factor through to the smallest, form an initial interval of positive integers. 1
 1, 2, 3, 5, 7, 11, 12, 13, 17, 19, 20, 23, 28, 29, 31, 37, 41, 43, 44, 45, 47, 52, 53, 59, 61, 63, 67, 68, 71, 73, 76, 79, 83, 89, 92, 97, 99, 101, 103, 107, 109, 113, 116, 117, 124, 127, 131, 137, 139, 148, 149, 151, 153, 157, 163, 164, 167, 171, 172, 173 (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), so these are Heinz numbers of integer partitions whose multiplicities, starting from the largest part through to the smallest, form an initial interval of positive integers. The enumeration of these partitions by sum is given by A179269. LINKS EXAMPLE The sequence of terms together with their prime indices begins:     1: {}     2: {1}     3: {2}     5: {3}     7: {4}    11: {5}    12: {1,1,2}    13: {6}    17: {7}    19: {8}    20: {1,1,3}    23: {9}    28: {1,1,4}    29: {10}    31: {11}    37: {12}    41: {13}    43: {14}    44: {1,1,5}    45: {2,2,3} MATHEMATICA Select[Range[100], Last/@If[#==1, {}, FactorInteger[#]]==Range[PrimeNu[#], 1, -1]&] CROSSREFS Cf. A055932, A056239, A098859, A109298, A112798, A130091, A179269, A317090, A325326, A325337, A325460. Sequence in context: A325337 A324515 A212127 * A028835 A028834 A070026 Adjacent sequences:  A307892 A307893 A307894 * A307896 A307897 A307898 KEYWORD nonn AUTHOR Gus Wiseman, May 04 2019 STATUS approved

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Last modified October 14 14:06 EDT 2019. Contains 328017 sequences. (Running on oeis4.)