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%I #5 Apr 08 2018 20:10:20
%S 165,273,325,351,495,525,561,595,675,741,765,819,825,931,1045,1053,
%T 1155,1173,1425,1485,1495,1575,1625,1653,1683,1771,1785,1815,1911,
%U 2025,2139,2145,2223,2275,2277,2295,2310,2415,2457,2465,2475,2625,2639,2695,2805,2945
%N Heinz numbers of integer partitions with more subset-products than subset-sums.
%C The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). A subset-sum (or subset-product) of a multiset y is any number equal to the sum (or product) of some submultiset of y.
%C Numbers n such that A301957(n) > A299701(n).
%e Sequence of partitions begins: (532), (642), (633), (6222), (5322), (4332), (752), (743), (33222), (862), (7322), (6422), (5332), (844), (853), (62222), (5432), (972), (8332), (53222), (963), (43322), (6333).
%t Select[Range[1000],With[{ptn=If[#===1,{},Join@@Cases[FactorInteger[#],{p_,k_}:>Table[PrimePi[p],{k}]]]},Length[Union[Times@@@Subsets[ptn]]]>Length[Union[Plus@@@Subsets[ptn]]]]&]
%Y Cf. A000712, A003963, A056239, A108917, A276024, A284640, A292886, A296150, A299701, A299702, A299729, A301854, A301855, A301856, A301957, A301979.
%K nonn
%O 1,1
%A _Gus Wiseman_, Mar 29 2018
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