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
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 21 2019
STATUS
approved