A365805 - OEIS

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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

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OFFSET

0,3

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

FORMULA

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

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

PROG

(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));

CROSSREFS