A365883 - OEIS

%I #15 Jan 10 2024 05:05:52

%S 4,12,20,27,28,36,44,52,60,68,76,84,92,100,108,116,124,132,135,140,

%T 148,156,164,172,180,188,189,196,204,212,220,228,236,244,252,260,268,

%U 276,284,292,297,300,308,316,324,332,340,348,351,356,364,372,380,388,396

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

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

%C 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.

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

%H Amiram Eldar, <a href="/A365883/b365883.txt">Table of n, a(n) for n = 1..10000</a>

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

%p filter:= proc(n) local F;

%p    F:= sort(ifactors(n)[2],(s,t) -> s[1]<t[1]);

%p    F[1][1]=F[1][2]

%p end proc:

%p select(filter, [$2..1000]); # _Robert Israel_, Sep 22 2023

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

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

%Y Cf. A020639, A051904.

%Y Subsequence of A100717 and A365889.

%Y Subsequences: A017113, A365884, A365885.

%K nonn,easy

%O 1,1

%A _Amiram Eldar_, Sep 22 2023