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A366279 The least number with same prime signature as A366275, where A366275(n) = A163511(A057889(n)).

%I A366279 #8 Oct 06 2023 21:24:07
%S A366279 1,2,4,2,8,4,6,2,16,8,12,6,12,4,6,2,32,16,24,12,36,12,30,6,24,8,12,6,
%T A366279 12,4,6,2,64,32,48,24,72,36,60,12,72,24,60,30,60,12,30,6,48,16,24,12,
%U A366279 36,12,30,6,24,8,12,6,12,4,6,2,128,64,96,48,144,72,120,24,216,72,180,60,180,36,60,12,144,48,120,60
%N A366279 The least number with same prime signature as A366275, where A366275(n) = A163511(A057889(n)).
%H A366279 Antti Karttunen, <a href="/A366279/b366279.txt">Table of n, a(n) for n = 0..16383</a>
%F A366279 a(n) = A046523(A366275(n)) = A046523(A163511(A057889(n))).
%F A366279 a(n) = A278531(A057889(n)).
%o A366279 (PARI)
%o A366279 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };
%o A366279 A030101(n) = if(n<1,0,subst(Polrev(binary(n)),x,2));
%o A366279 A057889(n) = if(!n,n,A030101(n/(2^valuation(n,2))) * (2^valuation(n, 2)));
%o A366279 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 A366279 A366275(n) = A163511(A057889(n));
%o A366279 A366279(n) = A046523(A366275(n));
%Y A366279 Cf. A046523, A057889, A163511, A278531, A366275, A366280 (rgs-transform).
%Y A366279 Cf. also A286601, A366261.
%K A366279 nonn
%O A366279 0,2
%A A366279 _Antti Karttunen_, Oct 06 2023