A366281 - OEIS

%I #9 Oct 07 2023 08:48:27

%S 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 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 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 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 Antti Karttunen, <a href="/A366281/b366281.txt">Table of n, a(n) for n = 0..65537</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

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

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

%o (PARI)

%o A030101(n) = if(n<1,0,subst(Polrev(binary(n)),x,2));

%o A057889(n) = if(!n,n,A030101(n/(2^valuation(n,2))) * (2^valuation(n, 2)));

%o 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 A366275(n) = A163511(A057889(n));

%o A052409(n) = { my(k=ispower(n)); if(k, k, n>1); };

%o A366281(n) = A052409(A366275(n));

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

%K nonn

%O 0,3

%A _Antti Karttunen_, Oct 06 2023