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A366278 Perfect powers k such that A052409(k) is equal to A052409(A366275(k)).

%I A366278 #15 Oct 07 2023 08:48:12
%S A366278 196,2116,2500,3136,3844,9409,15376,33856,37636,40000,49729,50176,
%T A366278 58564,64516,148225,150544,198916,229441,231361,237169,246016,255025,
%U A366278 528529,541696,543169,555025,592900,602176,628849,640000,654481,790321,795664,801025,802816,917764,925444,937024,948676,984064,1020100,1032256
%N A366278 Perfect powers k such that A052409(k) is equal to A052409(A366275(k)).
%C A366278 Numbers k such that A052409(k) > 1 and A052409(k) = A366281(k).
%C A366278 Conjecture: all terms are squares, and no higher powers occur.
%H A366278 Antti Karttunen, <a href="/A366278/b366278.txt">Table of n, a(n) for n = 1..408</a>
%o A366278 (PARI)
%o A366278 A030101(n) = if(n<1,0,subst(Polrev(binary(n)),x,2));
%o A366278 A057889(n) = if(!n,n,A030101(n/(2^valuation(n,2))) * (2^valuation(n, 2)));
%o A366278 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 A366278 A366275(n) = A163511(A057889(n));
%o A366278 A052409(n) = { my(k=ispower(n)); if(k, k, n>1); };
%o A366278 isA366278(n) = (A052409(n)>1 && A052409(n)==A052409(A366275(n)));
%Y A366278 Subsequence of A001597, and also by conjecture, of A153158 (thus also of A000290).
%Y A366278 Cf. A052409, A366275, A366281.
%Y A366278 Cf. also A365805, A365808.
%K A366278 nonn
%O A366278 1,1
%A A366278 _Antti Karttunen_, Oct 06 2023