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

1,1

Comments

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

Links

Table of n, a(n) for n=1..53.

Example

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}

Mathematica

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

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.

Sequence in context: A074915 A073461 A222618 * A056954 A246947 A226944

Adjacent sequences: A325989 A325990 A325991 * A325993 A325994 A325995

Keyword

nonn

Author

Gus Wiseman, Jun 02 2019

Status

approved