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

Author

Antti Karttunen, Sep 24 2016

Keywords

• nonn

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

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..5500 from Antti Karttunen)

Crossrefs

Cf. A109298, A276935.

Intersection with A276078 gives A276937.

Cf. A016825, A051063 (subsequences).

Complement of A325130.

Programs

Maple

q:= n-> ormap(i-> numtheory[pi](i[1])=i[2], ifactors(n)[2]):
select(q, [$1..225])[];  # Alois P. Heinz, Nov 18 2024

Mathematica

Select[Range[225], AnyTrue[FactorInteger[#], PrimePi[First[#1]] == Last[#1] &] &] (* Amiram Eldar, Jan 09 2021 *)