OFFSET
1,1
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 asymptotic density of this sequence is 1 - Product_{p in A006450} (1 - 1/p) = 1 - 1/(Sum_{n>=1} 1/A076610(n)) > 2/3. - Amiram Eldar, Feb 02 2021
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
A257994(a(n)) > 0.
EXAMPLE
The sequence of terms together with their prime indices begins:
3: {2}
5: {3}
6: {1,2}
9: {2,2}
10: {1,3}
11: {5}
12: {1,1,2}
15: {2,3}
17: {7}
18: {1,2,2}
20: {1,1,3}
21: {2,4}
22: {1,5}
24: {1,1,1,2}
25: {3,3}
27: {2,2,2}
30: {1,2,3}
31: {11}
33: {2,5}
34: {1,7}
MATHEMATICA
Select[Range[100], MemberQ[FactorInteger[#], {_?(PrimeQ@*PrimePi), _}]&]
CROSSREFS
Complement of A320628.
Positions of terms > 0 in A257994.
Positions of terms > 1 in A295665.
Primes of prime index are A006450.
Primes of nonprime index are A007821.
Products of primes of prime index are A076610.
Products of primes of nonprime index are A320628.
The number of nonprime prime indices is given by A330944.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 17 2020
STATUS
approved