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 the integer partitions counted by A276429.
The asymptotic density of this sequence is Product_{k>=1} (1 - 1/prime(k)^k + 1/prime(k)^(k+1)) = 0.68974964705635552968... - Amiram Eldar, Jan 09 2021
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..10000
EXAMPLE
The sequence of terms together with their prime indices begins:
1: {}
3: {2}
4: {1,1}
5: {3}
7: {4}
8: {1,1,1}
11: {5}
12: {1,1,2}
13: {6}
15: {2,3}
16: {1,1,1,1}
17: {7}
19: {8}
20: {1,1,3}
21: {2,4}
23: {9}
24: {1,1,1,2}
25: {3,3}
27: {2,2,2}
28: {1,1,4}
MAPLE
q:= n-> andmap(i-> numtheory[pi](i[1])<>i[2], ifactors(n)[2]):
a:= proc(n) option remember; local k; for k from 1+
`if`(n=1, 0, a(n-1)) while not q(k) do od; k
end:
seq(a(n), n=1..80); # Alois P. Heinz, Oct 28 2019
MATHEMATICA
Select[Range[100], And@@Cases[If[#==1, {}, FactorInteger[#]], {p_, k_}:>k!=PrimePi[p]]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 01 2019
STATUS
approved