A365883 Numbers k whose least prime divisor is equal to its exponent in the prime factorization of k.

4, 12, 20, 27, 28, 36, 44, 52, 60, 68, 76, 84, 92, 100, 108, 116, 124, 132, 135, 140, 148, 156, 164, 172, 180, 188, 189, 196, 204, 212, 220, 228, 236, 244, 252, 260, 268, 276, 284, 292, 297, 300, 308, 316, 324, 332, 340, 348, 351, 356, 364, 372, 380, 388, 396

Offset

1,1

Comments

Numbers k such that A020639(k) = A051904(k).

The asymptotic density of terms with least prime factor prime(n) (within all the positive integers) is d(n) = (1/prime(n)^prime(n) - 1/prime(n)^(prime(n)+1)) * Product_{k=1..(n-1)} (1-1/prime(k)). For example, for n = 1, 2, 3, 4 and 5, d(n) = 1/8, 1/81, 4/46875, 8/28824005 and 16/21968998637047.

The asymptotic density of this sequence is Sum_{n>=1} d(n) = 0.13743128989284883653... .

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

4 = 2^2 is a term since its least prime factor, 2, is equal to its exponent.

Maple

filter:= proc(n) local F;
   F:= sort(ifactors(n)[2], (s, t) -> s[1]<t[1]);
   F[1][1]=F[1][2]
end proc:
select(filter, [$2..1000]); # Robert Israel, Sep 22 2023

Mathematica

q[n_] := Equal @@ FactorInteger[n][[1]]; Select[Range[2, 400], q]

Prog

(PARI) is(n) = n > 1 && #Set(factor(n)[1, ]) == 1;

Crossrefs

Cf. A020639, A051904.

Subsequence of A100717 and A365889.

Subsequences: A017113, A365884, A365885.

Sequence in context: A273215 A273277 A100717 * A285526 A321466 A227226

Adjacent sequences: A365880 A365881 A365882 * A365884 A365885 A365886

Keyword

nonn,easy

Author

Amiram Eldar, Sep 22 2023

Status

approved