OFFSET
1,2
COMMENTS
A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798. The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), so these are Heinz numbers of integer partitions using factorial numbers. The enumeration of these partitions by sum is given by A064986.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
Sum_{n>=1} 1/a(n) = 1/Product_{k>=1} (1 - 1/prime(k!)) = 3.292606708493... . - Amiram Eldar, Dec 03 2022
EXAMPLE
The sequence of terms together with their prime indices begins:
1: {}
2: {1}
3: {2}
4: {1,1}
6: {1,2}
8: {1,1,1}
9: {2,2}
12: {1,1,2}
13: {6}
16: {1,1,1,1}
18: {1,2,2}
24: {1,1,1,2}
26: {1,6}
27: {2,2,2}
32: {1,1,1,1,1}
36: {1,1,2,2}
39: {2,6}
48: {1,1,1,1,2}
52: {1,1,6}
54: {1,2,2,2}
MATHEMATICA
nn=5;
facts=Array[Factorial, nn];
Select[Range[Prime[Max@@facts]], SubsetQ[facts, PrimePi/@First/@FactorInteger[#]]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 19 2019
STATUS
approved