A365886 - OEIS

%I #8 Sep 23 2023 15:01:40

%S 8,16,24,32,40,48,56,64,72,80,81,88,96,104,112,120,128,136,144,152,

%T 160,168,176,184,192,200,208,216,224,232,240,243,248,256,264,272,280,

%U 288,296,304,312,320,328,336,344,352,360,368,376,384,392,400,405,408,416

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

%C First differs from A185359 at n = 22.

%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)) * Product_{k=1..(n-1)} (1-1/prime(k)). For example, for n = 1, 2, 3, 4 and 5, d(n) = 1/8, 1/162, 1/46875, 4/86472015 and 8/109844993185235.

%C The asymptotic density of this sequence is Sum_{n>=1} d(n) = 0.13119421909731920416... .

%H Amiram Eldar, <a href="/A365886/b365886.txt">Table of n, a(n) for n = 1..10000</a>

%e 8 = 2^3 is a term since its least prime factor, 2, is smaller than its exponent, 3.

%t q[n_] := Less @@ FactorInteger[n][[1]]; Select[Range[2, 420], q]

%o (PARI) is(n) = {my(f = factor(n)); n > 1 && f[1, 1] < f[1, 2];}

%Y Cf. A020639, A051904.

%Y Subsequences: A008590 \ {0}, A365887, A365888.

%Y Subsequence of A185359.

%K nonn,easy

%O 1,1

%A _Amiram Eldar_, Sep 22 2023