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A326068 a(n) = n - sigma(A032742(n)), where sigma is the sum of divisors of n and A032742 gives the largest proper divisor of n.

%I A326068 #12 Dec 21 2024 11:09:33
%S A326068 0,1,2,1,4,2,6,1,5,4,10,0,12,6,9,1,16,5,18,2,13,10,22,-4,19,12,14,4,
%T A326068 28,6,30,1,21,16,27,-3,36,18,25,-2,40,10,42,8,21,22,46,-12,41,19,33,
%U A326068 10,52,14,43,0,37,28,58,-12,60,30,31,1,51,18,66,14,45,22,70,-19,72,36,44,16,65,22,78,-10,41,40,82,-12,67,42,57,4,88,12
%N A326068 a(n) = n - sigma(A032742(n)), where sigma is the sum of divisors of n and A032742 gives the largest proper divisor of n.
%H A326068 Antti Karttunen, <a href="/A326068/b326068.txt">Table of n, a(n) for n = 1..16384</a>
%H A326068 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>.
%F A326068 a(n) = n - A326065(n) = n - A000203(A032742(n)).
%F A326068 a(n) = A326067(n) + A033879(n).
%F A326068 Sum_{k=1..n} a(k) ~ ((1 - zeta(2) * c)/2) * n^2, where c = Sum_{p prime} ((p/((p-1)^2*(p+1))) * Product_{prime q <= p} ((q-1)^2*(q+1)/q^3)) = 0.307613599749... . - _Amiram Eldar_, Dec 21 2024
%o A326068 (PARI)
%o A326068 A032742(n) = if(1==n,n,n/vecmin(factor(n)[,1]));
%o A326068 A326065(n) = sigma(A032742(n));
%o A326068 A326068(n) = (n - A326065(n));
%Y A326068 Cf. A000203, A013661, A032742, A033879, A326065, A326066, A326067, A326069.
%K A326068 sign
%O A326068 1,3
%A A326068 _Antti Karttunen_, Jun 06 2019