A366281 a(n) = largest exponent m for which a representation of the form A366275(n) = k^m exists (for some k). a(0) = 0 by convention.

0, 1, 2, 1, 3, 2, 1, 1, 4, 3, 1, 1, 1, 2, 1, 1, 5, 4, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 6, 5, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 7, 6, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 2, 1, 1, 1, 1

Offset: 0

Author

Antti Karttunen, Oct 06 2023

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..65537
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A052409, A057889, A365805, A366275, A366278 [where a(n) = A052409(n)].

Programs

PARI

A030101(n) = if(n<1,0,subst(Polrev(binary(n)),x,2));
A057889(n) = if(!n,n,A030101(n/(2^valuation(n,2))) * (2^valuation(n, 2)));
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));
A366275(n) = A163511(A057889(n));
A052409(n) = { my(k=ispower(n)); if(k, k, n>1); };
A366281(n) = A052409(A366275(n));

Formula

a(n) = A052409(A366275(n)).

a(n) = A365805(A057889(n)).