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.

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

Adjacent sequences: A276933 A276934 A276935 * A276937 A276938 A276939

Keyword

nonn

Author

Antti Karttunen, Sep 24 2016

Status

approved