A325992 Heinz numbers of integer partitions such that not every ordered pair of distinct parts has a different difference.

30, 60, 90, 105, 110, 120, 150, 180, 210, 220, 238, 240, 270, 273, 300, 315, 330, 360, 385, 390, 420, 440, 450, 462, 476, 480, 506, 510, 525, 540, 546, 550, 570, 600, 627, 630, 660, 690, 714, 720, 735, 750, 770, 780, 806, 810, 819, 840, 858, 870, 880, 900, 910

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:
   30: {1,2,3}
   60: {1,1,2,3}
   90: {1,2,2,3}
  105: {2,3,4}
  110: {1,3,5}
  120: {1,1,1,2,3}
  150: {1,2,3,3}
  180: {1,1,2,2,3}
  210: {1,2,3,4}
  220: {1,1,3,5}
  238: {1,4,7}
  240: {1,1,1,1,2,3}
  270: {1,2,2,2,3}
  273: {2,4,6}
  300: {1,1,2,3,3}
  315: {2,2,3,4}
  330: {1,2,3,5}
  360: {1,1,1,2,2,3}
  385: {3,4,5}
  390: {1,2,3,6}
		

Crossrefs

The subset case is A143823.

The maximal case is A325879.

The integer partition case is A325858.

The strict integer partition case is A325876.

Heinz numbers of the counterexamples are given by A325992.

Cf. A002033, A056239, A108917, A112798, A143824, A325325, A325868, A325879, A325991, A325993, A325994.

Programs

Mathematica

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