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

1,1

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..44.

Example

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}

Mathematica

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

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.

Sequence in context: A242182 A136153 A069477 * A108573 A206653 A202429

Adjacent sequences: A325990 A325991 A325992 * A325994 A325995 A325996

Keyword

nonn

Author

Gus Wiseman, Jun 02 2019

Status

approved