OFFSET
1,1
COMMENTS
Numbers m with at least one prime factor such that the exponent of its highest power in m is equal to the index of that prime.
The asymptotic density of this sequence is 1 - Product_{k>=1} (1 - 1/prime(k)^k + 1/prime(k)^(k+1)) = 0.31025035294364447031... - Amiram Eldar, Jan 09 2021
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..5500 from Antti Karttunen)
EXAMPLE
2 is a member as 2 = prime(1) and as 2^1 divides but 2^2 does not divide 2.
3 is NOT a member as 3 = prime(2) but 3^2 does not divide 3.
4 is NOT a member as 2^2 divides 4.
6 is a member as 2 = prime(1) and 2^1 is a divisor of 6, but 2^2 is not.
9 is a member as 3 = prime(2) and 3^2 divides 9.
MATHEMATICA
Select[Range[225], AnyTrue[FactorInteger[#], PrimePi[First[#1]] == Last[#1] &] &] (* Amiram Eldar, Jan 09 2021 *)
PROG
(Scheme, with Antti Karttunen's IntSeq-library)
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Sep 24 2016
STATUS
approved