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A325782
Heinz numbers of strict perfect integer partitions.
13
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.
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.
Sequence in context: A375528 A270141 A294349 * A374891 A326343 A276453
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 21 2019
STATUS
approved