cp's OEIS Frontend

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.

%I A366281 #9 Oct 07 2023 08:48:27
%S A366281 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,
%T A366281 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,
%U A366281 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
%N 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.
%H A366281 Antti Karttunen, <a href="/A366281/b366281.txt">Table of n, a(n) for n = 0..65537</a>
%H A366281 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A366281 a(n) = A052409(A366275(n)).
%F A366281 a(n) = A365805(A057889(n)).
%o A366281 (PARI)
%o A366281 A030101(n) = if(n<1,0,subst(Polrev(binary(n)),x,2));
%o A366281 A057889(n) = if(!n,n,A030101(n/(2^valuation(n,2))) * (2^valuation(n, 2)));
%o A366281 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));
%o A366281 A366275(n) = A163511(A057889(n));
%o A366281 A052409(n) = { my(k=ispower(n)); if(k, k, n>1); };
%o A366281 A366281(n) = A052409(A366275(n));
%Y A366281 Cf. A052409, A057889, A365805, A366275, A366278 [where a(n) = A052409(n)].
%K A366281 nonn
%O A366281 0,3
%A A366281 _Antti Karttunen_, Oct 06 2023