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A325994 Heinz numbers of integer partitions such that not every ordered pair of distinct parts has a different quotient.

%I A325994 #5 Jun 02 2019 23:41:20
%S A325994 42,84,126,168,210,230,252,294,336,378,390,399,420,460,462,504,546,
%T A325994 588,630,672,690,714,742,756,780,798,840,882,920,924,966,1008,1050,
%U A325994 1092,1134,1150,1170,1176,1197,1218,1260,1302,1344,1365,1380,1386,1428,1470,1484
%N A325994 Heinz numbers of integer partitions such that not every ordered pair of distinct parts has a different quotient.
%C A325994 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%e A325994 The sequence of terms together with their prime indices begins:
%e A325994     42: {1,2,4}
%e A325994     84: {1,1,2,4}
%e A325994    126: {1,2,2,4}
%e A325994    168: {1,1,1,2,4}
%e A325994    210: {1,2,3,4}
%e A325994    230: {1,3,9}
%e A325994    252: {1,1,2,2,4}
%e A325994    294: {1,2,4,4}
%e A325994    336: {1,1,1,1,2,4}
%e A325994    378: {1,2,2,2,4}
%e A325994    390: {1,2,3,6}
%e A325994    399: {2,4,8}
%e A325994    420: {1,1,2,3,4}
%e A325994    460: {1,1,3,9}
%e A325994    462: {1,2,4,5}
%e A325994    504: {1,1,1,2,2,4}
%e A325994    546: {1,2,4,6}
%e A325994    588: {1,1,2,4,4}
%e A325994    630: {1,2,2,3,4}
%e A325994    672: {1,1,1,1,1,2,4}
%t A325994 Select[Range[1000],!UnsameQ@@Divide@@@Subsets[PrimePi/@First/@FactorInteger[#],{2}]&]
%Y A325994 The subset case is A325860.
%Y A325994 The maximal case is A325861.
%Y A325994 The integer partition case is A325853.
%Y A325994 The strict integer partition case is A325854.
%Y A325994 Heinz numbers of the counterexamples are given by A325994.
%Y A325994 Cf. A002033, A056239, A103300, A108917, A112798, A143823, A196724, A325768, A325856, A325868, A325869, A325876.
%K A325994 nonn
%O A325994 1,1
%A A325994 _Gus Wiseman_, Jun 02 2019