OFFSET
1,1
COMMENTS
The sequence is defined inductively as follows:
(a) it contains all numbers of the form 2^(2e) + 1, e >= 1,
and
(b) for any term a(n) and any e >= 0, (2^(2e+1) * a(n)) + 1 is also included as a term. There are no other kind of terms.
Contains no squares. See A365808 for a proof.
PROG
(PARI)
A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
isA365809(n) = (n%2 && issquare(A163511(n)));
(PARI)
A209229(n) = (n && !bitand(n, n-1));
isA365809(n) = if(n<=2, 0, my(v=valuation(n-1, 2)); if(A209229(n-1), !(v%2), (v%2)&&isA365809(n>>v)));
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 01 2023
STATUS
approved