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

1,2

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

Prog

(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));

Crossrefs

Subsequence of A005117.

Cf. A001651, A293430.

Sequence in context: A043089 A088952 A303541 * A032851 A102830 A031989

Adjacent sequences: A293520 A293521 A293522 * A293524 A293525 A293526

Keyword

nonn

Author

Antti Karttunen, Oct 11 2017

Status

approved