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A325398 Heinz numbers of reversed integer partitions whose k-th differences are strictly increasing for all k >= 0.

%I A325398 #6 May 03 2019 08:37:29
%S A325398 1,2,3,5,6,7,10,11,13,14,15,17,19,21,22,23,26,29,31,33,34,35,37,38,39,
%T A325398 41,42,43,46,47,51,53,55,57,58,59,61,62,65,66,67,69,71,73,74,77,78,79,
%U A325398 82,83,85,86,87,89,91,93,94,95,97,101,102,103,106,107,109
%N A325398 Heinz numbers of reversed integer partitions whose k-th differences are strictly increasing for all k >= 0.
%C A325398 First differs from A301899 in lacking 105. First differs from A325399 in having 42.
%C A325398 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%C A325398 The differences of a sequence are defined as if the sequence were increasing, so for example the differences of (6,3,1) are (-3,-2).
%C A325398 The zeroth differences of a sequence are the sequence itself, while the k-th differences for k > 0 are the differences of the (k-1)-th differences.
%C A325398 The enumeration of these partitions by sum is given by A325391.
%H A325398 Gus Wiseman, <a href="/A325325/a325325.txt">Sequences counting and ranking integer partitions by the differences of their successive parts.</a>
%e A325398 The sequence of terms together with their prime indices begins:
%e A325398     1: {}
%e A325398     2: {1}
%e A325398     3: {2}
%e A325398     5: {3}
%e A325398     6: {1,2}
%e A325398     7: {4}
%e A325398    10: {1,3}
%e A325398    11: {5}
%e A325398    13: {6}
%e A325398    14: {1,4}
%e A325398    15: {2,3}
%e A325398    17: {7}
%e A325398    19: {8}
%e A325398    21: {2,4}
%e A325398    22: {1,5}
%e A325398    23: {9}
%e A325398    26: {1,6}
%e A325398    29: {10}
%e A325398    31: {11}
%e A325398    33: {2,5}
%t A325398 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A325398 Select[Range[100],And@@Table[Less@@Differences[primeMS[#],k],{k,0,PrimeOmega[#]}]&]
%Y A325398 A subsequence of A005117.
%Y A325398 Cf. A056239, A112798, A325357, A325391, A325395, A325397, A325399, A325400, A325405, A325406, A325456, A325467.
%K A325398 nonn
%O A325398 1,2
%A A325398 _Gus Wiseman_, May 02 2019