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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.

%I A307895 #5 May 04 2019 08:31:15
%S A307895 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 A307895 61,63,67,68,71,73,76,79,83,89,92,97,99,101,103,107,109,113,116,117,
%U A307895 124,127,131,137,139,148,149,151,153,157,163,164,167,171,172,173
%N A307895 Numbers whose prime exponents, starting from the largest prime factor through to the smallest, form an initial interval of positive integers.
%C A307895 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 A307895 The sequence of terms together with their prime indices begins:
%e A307895     1: {}
%e A307895     2: {1}
%e A307895     3: {2}
%e A307895     5: {3}
%e A307895     7: {4}
%e A307895    11: {5}
%e A307895    12: {1,1,2}
%e A307895    13: {6}
%e A307895    17: {7}
%e A307895    19: {8}
%e A307895    20: {1,1,3}
%e A307895    23: {9}
%e A307895    28: {1,1,4}
%e A307895    29: {10}
%e A307895    31: {11}
%e A307895    37: {12}
%e A307895    41: {13}
%e A307895    43: {14}
%e A307895    44: {1,1,5}
%e A307895    45: {2,2,3}
%t A307895 Select[Range[100],Last/@If[#==1,{},FactorInteger[#]]==Range[PrimeNu[#],1,-1]&]
%Y A307895 Cf. A055932, A056239, A098859, A109298, A112798, A130091, A179269, A317090, A325326, A325337, A325460.
%K A307895 nonn
%O A307895 1,2
%A A307895 _Gus Wiseman_, May 04 2019