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

196, 2116, 2500, 3136, 3844, 9409, 15376, 33856, 37636, 40000, 49729, 50176, 58564, 64516, 148225, 150544, 198916, 229441, 231361, 237169, 246016, 255025, 528529, 541696, 543169, 555025, 592900, 602176, 628849, 640000, 654481, 790321, 795664, 801025, 802816, 917764, 925444, 937024, 948676, 984064, 1020100, 1032256

Offset: 1

Author

Antti Karttunen, Oct 06 2023

Keywords

• nonn

Comments

Numbers k such that A052409(k) > 1 and A052409(k) = A366281(k).

Conjecture: all terms are squares, and no higher powers occur.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..408

Crossrefs

Subsequence of A001597, and also by conjecture, of A153158 (thus also of A000290).

Cf. A052409, A366275, A366281.

Cf. also A365805, A365808.

Programs

PARI

A030101(n) = if(n<1,0,subst(Polrev(binary(n)),x,2));
A057889(n) = if(!n,n,A030101(n/(2^valuation(n,2))) * (2^valuation(n, 2)));
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));
A366275(n) = A163511(A057889(n));
A052409(n) = { my(k=ispower(n)); if(k, k, n>1); };
isA366278(n) = (A052409(n)>1 && A052409(n)==A052409(A366275(n)));