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A325993 Heinz numbers of integer partitions such that not every orderless pair of distinct parts has a different product.

%I A325993 #9 Jun 02 2019 23:41:13
%S A325993 390,780,798,1170,1365,1560,1596,1914,1950,2340,2394,2590,2730,2886,
%T A325993 3120,3192,3510,3828,3900,3990,4095,4290,4386,4485,4680,4788,5070,
%U A325993 5170,5180,5460,5586,5742,5772,5850,6042,6240,6384,6630,6699,6825,7020,7182,7410,7656
%N A325993 Heinz numbers of integer partitions such that not every orderless pair of distinct parts has a different product.
%C A325993 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%e A325993 The sequence of terms together with their prime indices begins:
%e A325993    390: {1,2,3,6}
%e A325993    780: {1,1,2,3,6}
%e A325993    798: {1,2,4,8}
%e A325993   1170: {1,2,2,3,6}
%e A325993   1365: {2,3,4,6}
%e A325993   1560: {1,1,1,2,3,6}
%e A325993   1596: {1,1,2,4,8}
%e A325993   1914: {1,2,5,10}
%e A325993   1950: {1,2,3,3,6}
%e A325993   2340: {1,1,2,2,3,6}
%e A325993   2394: {1,2,2,4,8}
%e A325993   2590: {1,3,4,12}
%e A325993   2730: {1,2,3,4,6}
%e A325993   2886: {1,2,6,12}
%e A325993   3120: {1,1,1,1,2,3,6}
%e A325993   3192: {1,1,1,2,4,8}
%e A325993   3510: {1,2,2,2,3,6}
%e A325993   3828: {1,1,2,5,10}
%e A325993   3900: {1,1,2,3,3,6}
%e A325993   3990: {1,2,3,4,8}
%t A325993 Select[Range[1000],!UnsameQ@@Times@@@Subsets[PrimePi/@First/@FactorInteger[#],{2}]&]
%Y A325993 The subset case is A196724.
%Y A325993 The maximal case is A325859.
%Y A325993 The integer partition case is A325856.
%Y A325993 The strict integer partition case is A325855.
%Y A325993 Heinz numbers of the counterexamples are given by A325993.
%Y A325993 Cf. A002033, A056239, A108917, A112798, A143823, A292886, A325858, A325877, A325991, A325992, A325994.
%K A325993 nonn
%O A325993 1,1
%A A325993 _Gus Wiseman_, Jun 02 2019