A365805 a(n) = largest exponent m for which a representation of the form A163511(n) = k^m exists (for some k). a(0) = 0 by convention.

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

Offset: 0

Author

Antti Karttunen, Oct 01 2023

Keywords

• nonn

Comments

Equivalently, the largest exponent m for which a representation of the form A332214(n) = k^m exists (for some k), or similarly, for any other such variant of A163511, like A332817.

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, A163511, A332214, A332817, A365807, A366370.

Cf. A365808 (positions of even terms), A365801 (multiples of 3), A365802 (multiples of 5), A366287 (multiples of 7), A366391 (multiples of 11).

Programs

PARI

A052409(n) = { my(k=ispower(n)); if(k, k, n>1); };
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));
A365805(n) = A052409(A163511(n));

Formula

a(n) = A052409(A163511(n)).

If a(n) > 1 (or A052409(n) > 1), then a(n) <> A052409(n). [Consider A366370]