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%I #5 May 04 2019 08:31:15
%S 1,2,3,5,7,11,12,13,17,19,20,23,28,29,31,37,41,43,44,45,47,52,53,59,
%T 61,63,67,68,71,73,76,79,83,89,92,97,99,101,103,107,109,113,116,117,
%U 124,127,131,137,139,148,149,151,153,157,163,164,167,171,172,173
%N Numbers whose prime exponents, starting from the largest prime factor through to the smallest, form an initial interval of positive integers.
%C 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.
%e The sequence of terms together with their prime indices begins:
%e 1: {}
%e 2: {1}
%e 3: {2}
%e 5: {3}
%e 7: {4}
%e 11: {5}
%e 12: {1,1,2}
%e 13: {6}
%e 17: {7}
%e 19: {8}
%e 20: {1,1,3}
%e 23: {9}
%e 28: {1,1,4}
%e 29: {10}
%e 31: {11}
%e 37: {12}
%e 41: {13}
%e 43: {14}
%e 44: {1,1,5}
%e 45: {2,2,3}
%t Select[Range[100],Last/@If[#==1,{},FactorInteger[#]]==Range[PrimeNu[#],1,-1]&]
%Y Cf. A055932, A056239, A098859, A109298, A112798, A130091, A179269, A317090, A325326, A325337, A325460.
%K nonn
%O 1,2
%A _Gus Wiseman_, May 04 2019
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