A325782 Heinz numbers of strict perfect integer partitions.

1, 2, 6, 42, 798, 42294, 5540514, 1723099854, 1238908795026, 2005793339147094, 7363267348008982074, 60091624827101302705914, 1073416694286510570235741782, 41726927156999525396773990291686, 3505771238949629125260760342336582662

Offset: 1

Author

Gus Wiseman, May 21 2019

Keywords

• nonn

Comments

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

The sum of prime indices of n is A056239(n). A number is in this sequence iff it is squarefree, all of its divisors have distinct sums of prime indices, and these sums cover an initial interval of nonnegative integers. For example, the divisors of 42 are {1, 2, 3, 6, 7, 14, 21, 42}, with respective sums of prime indices {0, 1, 2, 3, 4, 5, 6, 7}, so 42 is in the sequence.

Examples

			The sequence of terms together with their prime indices begins:
      1: {}
      2: {1}
      6: {1,2}
     42: {1,2,4}
    798: {1,2,4,8}
  42294: {1,2,4,8,16}
		

Crossrefs

A subsequence of A005117, A299702, and A325781.

Cf. A002033, A056239, A108917, A112798, A126796, A188431, A325780.

Programs

Mathematica

Table[Times@@Prime[2^Range[0,n-1]],{n,0,10}]

Formula

a(n) = Product_{i = 0..n-1} prime(2^i).