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

390, 780, 798, 1170, 1365, 1560, 1596, 1914, 1950, 2340, 2394, 2590, 2730, 2886, 3120, 3192, 3510, 3828, 3900, 3990, 4095, 4290, 4386, 4485, 4680, 4788, 5070, 5170, 5180, 5460, 5586, 5742, 5772, 5850, 6042, 6240, 6384, 6630, 6699, 6825, 7020, 7182, 7410, 7656

Offset: 1

Author

Gus Wiseman, Jun 02 2019

Keywords

• nonn

Comments

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

Examples

			The sequence of terms together with their prime indices begins:
   390: {1,2,3,6}
   780: {1,1,2,3,6}
   798: {1,2,4,8}
  1170: {1,2,2,3,6}
  1365: {2,3,4,6}
  1560: {1,1,1,2,3,6}
  1596: {1,1,2,4,8}
  1914: {1,2,5,10}
  1950: {1,2,3,3,6}
  2340: {1,1,2,2,3,6}
  2394: {1,2,2,4,8}
  2590: {1,3,4,12}
  2730: {1,2,3,4,6}
  2886: {1,2,6,12}
  3120: {1,1,1,1,2,3,6}
  3192: {1,1,1,2,4,8}
  3510: {1,2,2,2,3,6}
  3828: {1,1,2,5,10}
  3900: {1,1,2,3,3,6}
  3990: {1,2,3,4,8}
		

Crossrefs

The subset case is A196724.

The maximal case is A325859.

The integer partition case is A325856.

The strict integer partition case is A325855.

Heinz numbers of the counterexamples are given by A325993.

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

Programs

Mathematica

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