A293523 Persistently squarefree numbers for base-3 shifting: Numbers n such that all terms in finite set of positive numbers [n, floor(n/3), floor(n/9), floor(n/27), ..., floor(n/3^k)>0] are squarefree.

1, 2, 3, 5, 6, 7, 10, 11, 15, 17, 19, 21, 22, 23, 30, 31, 33, 34, 35, 46, 47, 51, 53, 57, 58, 59, 65, 66, 67, 69, 70, 71, 91, 93, 94, 95, 101, 102, 103, 105, 106, 107, 138, 139, 141, 142, 143, 154, 155, 159, 161, 173, 174, 177, 178, 179, 195, 197, 199, 201, 202, 203, 209, 210, 211, 213, 214, 215, 273, 274, 281, 282

Offset: 1

Author

Antti Karttunen, Oct 11 2017

Keywords

• nonn

Comments

If there is any number present which itself is not divisible by 3 (is in A001651), then 3n is also present in this sequence.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A005117.

Cf. A001651, A293430.

Programs

PARI

\\ A naivish algorithm:
allocatemem(2^30);
up_to_level = 10;
up_to = (3^(1+up_to_level))-1;
vekkuli = vector(up_to);
vekkuli[1] = 1;
vekkuli[2] = -1;
write("b293523.txt", 1, " ", 1);
write("b293523.txt", 2, " ", 2);
kA293523 = 3; for(n=3,up_to, vekkuli[n] = moebius(n)*vekkuli[n\3]; if(vekkuli[n],write("b293523.txt", kA293523, " ", n); kA293523++;));

PARI

is_persistently_squarefree(n,base) = { while(n>1, if(!issquarefree(n),return(0)); n \= base); (1); };
isA293523(n) = is_persistently_squarefree(n,3);
n=0; k=1; while(k <= 10000, n=n+1; if(isA293523(n),write("b293523.txt", k, " ", n);k=k+1));