OFFSET
1,1
COMMENTS
Numbers k such that k, k+1 and k+2 are all terms of A365869.
Numbers of the form 4*k+2 are not terms of A365869. 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 = 3, 4, ..., are 1, 18, 195, 1952, 19542, 195514, 1955859, 19560453, 195611458, ... . Apparently, the asymptotic density of this sequence exists and equals 0.001956... .
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
475 is a term since the exponent of the prime factor 5 in the factorization 475 = 5^2 * 19 is 2, which is even, the exponent of the prime factor 2 in the factorization 476 = 2^2 * 7 * 17 is 2, which is even, and the exponent of the prime factor 3 in the factorization 477 = 3^2 * 53 is also 2, which is even.
MATHEMATICA
Select[4 * Range[6000] + 3, AllTrue[# + {0, 1, 2}, EvenQ[FactorInteger[#1][[1, -1]]] &] &]
PROG
(PARI) is(n) = !(factor(n)[1, 2]%2);
lista(kmax) = forstep(k = 3, kmax, 4, if(is(k) && is(k+1) && is(k+2), print1(k, ", ")));
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Sep 21 2023
STATUS
approved