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A365883
Numbers k whose least prime divisor is equal to its exponent in the prime factorization of k.
4
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
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
Subsequence of A100717 and A365889.
Subsequences: A017113, A365884, A365885.
Sequence in context: A273215 A273277 A100717 * A285526 A321466 A227226
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Sep 22 2023
STATUS
approved