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A324185 Deficiency of n permuted by A163511: a(n) = A033879(A163511(n)) = 2*A163511(n) - sigma(A163511(n)).

%I A324185 #25 Oct 24 2023 12:21:09
%S A324185 1,1,1,2,1,5,0,4,1,14,-3,19,-4,6,2,6,1,41,-12,94,-19,26,7,41,-12,12,
%T A324185 -12,22,-2,10,4,10,1,122,-39,469,-64,126,32,286,-51,47,-72,148,-17,66,
%U A324185 25,109,-28,30,-54,102,-48,18,-4,58,-10,22,-12,38,0,18,8,12,1,365,-120,2344,-199,626,157,2001,-168,222,-372,1030,-92,458,172,1198
%N A324185 Deficiency of n permuted by A163511: a(n) = A033879(A163511(n)) = 2*A163511(n) - sigma(A163511(n)).
%C A324185 If there are no odd perfect numbers, then all n for which a(n) is 0 are given by sequence A324200.
%H A324185 Antti Karttunen, <a href="/A324185/b324185.txt">Table of n, a(n) for n = 0..16384</a>
%H A324185 Antti Karttunen, <a href="/A324185/a324185.txt">Data supplement: n, a(n) computed for n = 0..65537</a>
%F A324185 a(n) = A033879(A163511(n)) = 2*A163511(n) - A324184(n) = 2*A163511(n) - A000203(A163511(n)).
%F A324185 For n > 0, a(n) = A324055(A054429(n)).
%o A324185 (PARI)
%o A324185 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 A324185 A033879(n) = (2*n-sigma(n));
%o A324185 A324185(n) = A033879(A163511(n));
%o A324185 (PARI)
%o A324185 A324184(n) = if(!n,1,my(p=2,mp=p*p,m=1); while(n>1, if(n%2, p=nextprime(1+p); mp = p*p, if((2==n)||!(n%4),mp *= p,m *= (mp-1)/(p-1))); n >>= 1); (m*(mp-1)/(p-1)));
%o A324185 A324185(n) = (2*A163511(n)) - A324184(n);
%Y A324185 Cf. A000203, A033879, A054429, A163511, A324055, A324182 (compare the scatter plot), A324184, A324187, A324188, A324189, A324199, A324200.
%K A324185 sign,look
%O A324185 0,4
%A A324185 _Antti Karttunen_, Feb 17 2019