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A276936
Numbers m with at least one distinct prime factor prime(k) such that prime(k)^k divides, but prime(k)^(k+1) does not divide m.
5
2, 6, 9, 10, 14, 18, 22, 26, 30, 34, 36, 38, 42, 45, 46, 50, 54, 58, 62, 63, 66, 70, 72, 74, 78, 82, 86, 90, 94, 98, 99, 102, 106, 110, 114, 117, 118, 122, 125, 126, 130, 134, 138, 142, 144, 146, 150, 153, 154, 158, 162, 166, 170, 171, 174, 178, 180, 182, 186, 190, 194, 198, 202, 206, 207, 210, 214, 218, 222, 225
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)
(define A276936 (NONZERO-POS 1 1 A276935))
CROSSREFS
Cf. A276935.
Intersection with A276078 gives A276937.
Cf. A016825, A051063 (subsequences).
Complement of A325130.
Sequence in context: A360136 A359821 A047396 * A276937 A243373 A085304
KEYWORD
nonn
AUTHOR
Antti Karttunen, Sep 24 2016
STATUS
approved