OFFSET
1,2
COMMENTS
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..10000
EXAMPLE
For 479 we see that 479 is prime (thus squarefree, in A005117), [479/2] = 239 is also a prime, [239/2] = 119 = 7*17 (a squarefree composite), [119/2] = 59 (a prime), [59/2] = 29 (a prime), [29/2] = 14 = 2*7 (a squarefree composite), [14/2] = 7 (a prime), [7/2] = 3 (a prime), [3/2] = 1 (the end of halving process 1 is also squarefree), thus all the values obtained by repeated halving were squarefree and 479 is a member of this sequence. Here [ ] stands for taking floor.
MATHEMATICA
With[{s = Fold[Append[#1, MoebiusMu[#2] #1[[Floor[#2/2]]]] &, {1}, Range[2, 480]]}, Flatten@ Position[s, _?(# != 0 &)]] (* Michael De Vlieger, Oct 10 2017 *)
PROG
(PARI)
is_persistently_squarefree(n, base) = { while(n>1, if(!issquarefree(n), return(0)); n \= base); (1); };
isA293430(n) = is_persistently_squarefree(n, 2);
n=0; k=1; while(k <= 10000, n=n+1; if(isA293430(n), write("b293430.txt", k, " ", n); k=k+1)); \\ Antti Karttunen, Oct 11 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen and Michael De Vlieger, Oct 10 2017
STATUS
approved