A325782 Heinz numbers of strict perfect integer partitions.

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

Offset

1,2

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.

Links

Table of n, a(n) for n=1..15.

Formula

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

Example

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}

Mathematica

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

Crossrefs

A subsequence of A005117, A299702, and A325781.

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

Sequence in context: A061062 A270141 A294349 * A326343 A276453 A152479

Adjacent sequences: A325779 A325780 A325781 * A325783 A325784 A325785

Keyword

nonn

Author

Gus Wiseman, May 21 2019

Status

approved