OFFSET
1,1
COMMENTS
Numbers of the form 4*k+2 are not terms of A365883. Therefore there are no runs of 4 or more consecutive integers.
Since the middle integer in each triple is not divisible by 8, all the terms of this sequence are of the form 8*k+3.
The numbers of terms not exceeding 10^k, for k = 6, 7, ..., are 2, 16, 158, 1585, 15853, 158540, ... . Apparently, the asymptotic density of this sequence exists and equals 1.585...*10^(-6).
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
228123 = 3^3 * 7 * 17 * 71 is a term since its least prime factor, 3, is equal to its exponent, the least prime factor of 228123 = 2^2 * 13 * 41 * 107, 2, is equal to its exponent, and the least prime factor of 228125 = 5^5 * 73, 5, is also equal to its exponent.
MATHEMATICA
q[n_] := Equal @@ FactorInteger[n][[1]]; Select[8*Range[125000] + 3, AllTrue[# + {0, 1, 2}, q] &]
PROG
(PARI) is(n) = #Set(factor(n)[1, ]) == 1;
lista(kmax) = forstep(k = 3, kmax, 8, if(is(k) && is(k+1) && is(k+2), print1(k, ", ")));
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Sep 22 2023
STATUS
approved