cp's OEIS Frontend

A365889 Numbers k whose least prime divisor divides its exponent in the prime factorization of k.

%I A365889 #13 Mar 28 2025 03:25:56
%S A365889 4,12,16,20,27,28,36,44,48,52,60,64,68,76,80,84,92,100,108,112,116,
%T A365889 124,132,135,140,144,148,156,164,172,176,180,188,189,192,196,204,208,
%U A365889 212,220,228,236,240,244,252,256,260,268,272,276,284,292,297,300,304,308
%N A365889 Numbers k whose least prime divisor divides its exponent in the prime factorization of k.
%C A365889 Numbers k such that A020639(k) | A051904(k).
%C A365889 The asymptotic density of terms with least prime factor prime(n) (within all the positive integers) is d(n) = ((prime(n)-1)/(prime(n)*(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) = 1/6, 1/78, 1/11715, 4/14411985 and 8/10984499318485.
%C A365889 The asymptotic density of this sequence is Sum_{n>=1} d(n) = 0.17957281768342725732... .
%H A365889 Amiram Eldar, <a href="/A365889/b365889.txt">Table of n, a(n) for n = 1..10000</a>
%e A365889 4 = 2^2 is a term since its least prime factor, 2, divides its exponent, 2.
%e A365889 16 = 2^4 is a term since its least prime factor, 2, divides its exponent, 4.
%t A365889 q[n_] := Divisible @@ Reverse[FactorInteger[n][[1]]]; Select[Range[2, 400], q]
%o A365889 (PARI) is(n) = {my(f = factor(n)); n > 1 && !(f[1, 2] % f[1, 1]);}
%Y A365889 Cf. A020639, A051904.
%Y A365889 Subsequence of A342090.
%Y A365889 Subsequences: A365883, A365890, A365891.
%K A365889 nonn,easy
%O A365889 1,1
%A A365889 _Amiram Eldar_, Sep 22 2023