OFFSET
1,1
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).
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
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.
MATHEMATICA
q[n_] := Divisible @@ Reverse[FactorInteger[n][[1]]]; Select[4 * Range[2*10^6] + 3, AllTrue[# + {0, 1, 2}, q] &]
PROG
(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, ", ")));
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Sep 22 2023
STATUS
approved