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A366885 Dedekind psi function applied to the odd part of n, permuted by A163511: a(n) = A347385(A163511(n)).

%I A366885 #7 Nov 04 2023 14:00:33
%S A366885 1,1,1,4,1,12,4,6,1,36,12,30,4,24,6,8,1,108,36,150,12,120,30,56,4,72,
%T A366885 24,48,6,32,8,12,1,324,108,750,36,600,150,392,12,360,120,336,30,224,
%U A366885 56,132,4,216,72,240,24,192,48,96,6,96,32,72,8,48,12,14,1,972,324,3750,108,3000,750,2744,36,1800,600,2352
%N A366885 Dedekind psi function applied to the odd part of n, permuted by A163511: a(n) = A347385(A163511(n)).
%H A366885 Antti Karttunen, <a href="/A366885/b366885.txt">Table of n, a(n) for n = 0..16384</a>
%o A366885 (PARI)
%o A366885 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 A366885 A347385(n) = if(1==n,n, my(f=factor(n>>valuation(n, 2))); prod(i=1, #f~, f[i, 1]^f[i, 2] + f[i, 1]^(f[i, 2]-1)));
%o A366885 A366885(n) = A347385(A163511(n));
%Y A366885 Cf. A001615, A163511, A347385, A366886 (rgs-transform).
%Y A366885 Cf. also A324186.
%K A366885 nonn
%O A366885 0,4
%A A366885 _Antti Karttunen_, Nov 04 2023