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A354207 a(n) = n - A354203(sigma(A354202(n))), where A354202 is fully multiplicative with a(p) = A354200(A000720(p)), and A354203 is its left inverse.

%I A354207 #10 May 24 2022 16:32:00
%S A354207 0,1,2,-19,2,5,6,3,-2,7,9,-11,12,13,12,-453,15,7,18,-49,20,20,22,19,
%T A354207 -28,25,23,5,18,27,24,-37,31,32,32,-217,34,37,38,25,40,41,42,-2,12,45,
%U A354207 45,-421,16,-3,49,29,30,50,49,51,56,47,46,-9,32,55,52,-19443,62,64,66,22,68,67,69,17,71,71,22,53,75,77,76
%N A354207 a(n) = n - A354203(sigma(A354202(n))), where A354202 is fully multiplicative with a(p) = A354200(A000720(p)), and A354203 is its left inverse.
%H A354207 Antti Karttunen, <a href="/A354207/b354207.txt">Table of n, a(n) for n = 1..20000</a>
%H A354207 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A354207 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A354207 a(n) = n - A354206(n).
%o A354207 (PARI)
%o A354207 A354200(n) = if(1==n,5,my(p=prime(n), m=p%4); forprime(q=1+p,,if(m==(q%4),return(q))));
%o A354207 A354201(n) = if(n<=3,(n+1)\2,my(m=prime(n)%4); forstep(i=n-1,0,-1,if(m==(prime(i)%4),return(prime(i)))));
%o A354207 A354202(n) = { my(f=factor(n)); for(k=1,#f~,f[k,1] = A354200(primepi(f[k,1]))); factorback(f); };
%o A354207 A354203(n) = { my(f=factor(n)); for(k=1,#f~,f[k,1] = A354201(primepi(f[k,1]))); factorback(f); };
%o A354207 A354207(n) = (n-A354203(sigma(A354202(n))));
%Y A354207 Cf. A000203, A354200, A354201, A354202, A354203, A354205, A354206.
%Y A354207 Cf. also A348736.
%K A354207 sign
%O A354207 1,3
%A A354207 _Antti Karttunen_, May 23 2022