A365891 Starts of run of 3 consecutive integers that are terms of A365889.

228123, 446875, 903123, 1121875, 1240623, 2253123, 2928123, 3146875, 3821875, 3940623, 4159375, 4278123, 5846875, 6303123, 6978123, 7196875, 7871875, 9003123, 9221875, 9340623, 9896875, 10353123, 10909375, 11028123, 11246875, 12040623, 12259375, 12378123, 13053123

Offset: 1

Author

Amiram Eldar, Sep 22 2023

Keywords

• nonn

Comments

Numbers of the form 4*k+2 are not terms of A365889. Therefore there are no runs of 4 or more consecutive integers, and all the terms of this sequence are of the form 4*k+3.

The numbers of terms not exceeding 10^k, for k = 6, 7, ..., are 3, 21, 220, 2193, 21954, 219583, ... . Apparently, the asymptotic density of this sequence exists and equals 2.195...*10^(-6).

Examples

			446875 = 5^5 * 11 * 13 is a term since its least prime factor, 5, divides it exponent, 5, the least prime factor of 446876 = 2^2 * 47 * 2377, 2, divides its exponent, 2, and the least prime factor of 446877 = 3^6 * 613, 3, also divides its exponent, 6.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A004767, A365889 and A365890.

A365885 is a subsequence.

Programs

Mathematica

q[n_] := Divisible @@ Reverse[FactorInteger[n][[1]]]; Select[4 * Range[2*10^6] + 3, AllTrue[# + {0, 1, 2}, q] &]

PARI

is(n) = {my(f = factor(n)); n > 1 && !(f[1, 2] % f[1, 1]);}
lista(kmax) = forstep(k = 3, kmax, 4, if(is(k) && is(k+1) && is(k+2), print1(k, ", ")));