A325993 - OEIS

%I #9 Jun 02 2019 23:41:13

%S 390,780,798,1170,1365,1560,1596,1914,1950,2340,2394,2590,2730,2886,

%T 3120,3192,3510,3828,3900,3990,4095,4290,4386,4485,4680,4788,5070,

%U 5170,5180,5460,5586,5742,5772,5850,6042,6240,6384,6630,6699,6825,7020,7182,7410,7656

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

%C The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).

%e The sequence of terms together with their prime indices begins:

%e    390: {1,2,3,6}

%e    780: {1,1,2,3,6}

%e    798: {1,2,4,8}

%e   1170: {1,2,2,3,6}

%e   1365: {2,3,4,6}

%e   1560: {1,1,1,2,3,6}

%e   1596: {1,1,2,4,8}

%e   1914: {1,2,5,10}

%e   1950: {1,2,3,3,6}

%e   2340: {1,1,2,2,3,6}

%e   2394: {1,2,2,4,8}

%e   2590: {1,3,4,12}

%e   2730: {1,2,3,4,6}

%e   2886: {1,2,6,12}

%e   3120: {1,1,1,1,2,3,6}

%e   3192: {1,1,1,2,4,8}

%e   3510: {1,2,2,2,3,6}

%e   3828: {1,1,2,5,10}

%e   3900: {1,1,2,3,3,6}

%e   3990: {1,2,3,4,8}

%t Select[Range[1000],!UnsameQ@@Times@@@Subsets[PrimePi/@First/@FactorInteger[#],{2}]&]

%Y The subset case is A196724.

%Y The maximal case is A325859.

%Y The integer partition case is A325856.

%Y The strict integer partition case is A325855.

%Y Heinz numbers of the counterexamples are given by A325993.

%Y Cf. A002033, A056239, A108917, A112798, A143823, A292886, A325858, A325877, A325991, A325992, A325994.

%K nonn

%O 1,1

%A _Gus Wiseman_, Jun 02 2019