cp's OEIS Frontend

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.

%I A365805 #21 Nov 23 2023 15:12:51
%S A365805 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,
%T A365805 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,
%U A365805 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
%N 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.
%C A365805 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.
%H A365805 Antti Karttunen, <a href="/A365805/b365805.txt">Table of n, a(n) for n = 0..65537</a>
%H A365805 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A365805 a(n) = A052409(A163511(n)).
%F A365805 If a(n) > 1 (or A052409(n) > 1), then a(n) <> A052409(n). [Consider A366370]
%o A365805 (PARI)
%o A365805 A052409(n) = { my(k=ispower(n)); if(k, k, n>1); };
%o A365805 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 A365805 A365805(n) = A052409(A163511(n));
%Y A365805 Cf. A052409, A163511, A332214, A332817, A365807, A366370.
%Y A365805 Cf. A365808 (positions of even terms), A365801 (multiples of 3), A365802 (multiples of 5), A366287 (multiples of 7), A366391 (multiples of 11).
%K A365805 nonn
%O A365805 0,3
%A A365805 _Antti Karttunen_, Oct 01 2023