A365889 - OEIS

%I #22 Jan 17 2026 13:19:42

%S 4,12,16,20,27,28,36,44,48,52,60,64,68,76,80,84,92,100,108,112,116,

%T 124,132,135,140,144,148,156,164,172,176,180,188,189,192,196,204,208,

%U 212,220,228,236,240,244,252,256,260,268,272,276,284,292,297,300,304,308

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

%C Numbers k such that A020639(k) | A067029(k). - The second A-number corrected by _Antti Karttunen_, Jan 16 2026.

%C 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 The asymptotic density of this sequence is Sum_{n>=1} d(n) = 0.17957281768342725732... .

%C Numbers k such that A053669(A276085(k)) is not A020639(k). - _Antti Karttunen_, Jan 16 2026

%H Amiram Eldar, <a href="/A365889/b365889.txt">Table of n, a(n) for n = 1..10000</a>

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

%e 16 = 2^4 is a term since its least prime factor, 2, divides its exponent, 4.

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

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

%Y Cf. A020639, A053669, A067029, A276085.

%Y Subsequence of A342090, which is a subsequence of A100716.

%Y Subsequences: A108269 (even terms), A365883, A365890, A365891.

%K nonn,easy

%O 1,1

%A _Amiram Eldar_, Sep 22 2023