

A365868


Starts of runs of 3 consecutive integers that are divisible by the cube of their least prime factor.


3



1375, 16119, 25623, 28375, 52623, 55375, 57967, 79623, 82375, 90207, 94471, 106623, 109375, 129623, 133623, 134431, 136375, 160623, 163375, 164295, 187623, 190375, 206143, 214623, 217375, 241623, 244375, 268623, 271375, 280231, 295623, 298375, 312471, 322623, 325375
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

Numbers k such that k, k+1 and k+2 are all terms of A365866.
Numbers of the form 4*k+2 are not terms of A365866. Therefore, there are no runs of 4 or more consecutive integers. Since the middle integer in each triple is divisible by 8, all the terms of this sequence are of the form 8*k+7.
The numbers of terms not exceeding 10^k, for k = 4, 5, ..., are , 1, 11, 109, 1092, 10899, 109125, 1091335, 10912897, ... . Apparently, the asymptotic density of this sequence exists and equals 0.0001091... .


LINKS



EXAMPLE

1375 is a term since 5 is the least prime factor of 1375 and 1375 is divisible by 5^3 = 125, 2 is the least prime factor of 1376 and 1376 is divisible by 2^3 = 8, and 3 is the least prime factor of 1377 and 1377 is divisible by 3^3 = 27.


MATHEMATICA

Select[8 * Range[41000] + 7, AllTrue[# + {0, 1, 2}, FactorInteger[#1][[1, 1]] >= 3 &] &]


PROG

(PARI) is(n) = factor(n)[1, 2] >= 3;
lista(kmax) = forstep(k = 7, kmax, 8, if(is(k) && is(k+1) && is(k+2), print1(k, ", ")));


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



