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A331386
Numbers with at least one prime prime index.
8
3, 5, 6, 9, 10, 11, 12, 15, 17, 18, 20, 21, 22, 24, 25, 27, 30, 31, 33, 34, 35, 36, 39, 40, 41, 42, 44, 45, 48, 50, 51, 54, 55, 57, 59, 60, 62, 63, 65, 66, 67, 68, 69, 70, 72, 75, 77, 78, 80, 81, 82, 83, 84, 85, 87, 88, 90, 93, 95, 96, 99, 100, 102, 105, 108
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
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.
Sequence in context: A161182 A267312 A362579 * A331916 A371127 A269390
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 17 2020
STATUS
approved