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A326067 a(n) = sigma(n) - sigma(A032742(n)) - n, where A032742 gives the largest proper divisor of n, and sigma is the sum of divisors of n.

%I A326067 #18 Dec 21 2024 11:09:47
%S A326067 -1,0,0,0,0,2,0,0,0,2,0,4,0,2,3,0,0,8,0,4,3,2,0,8,0,2,0,4,0,18,0,0,3,
%T A326067 2,5,16,0,2,3,8,0,22,0,4,9,2,0,16,0,12,3,4,0,26,5,8,3,2,0,36,0,2,9,0,
%U A326067 5,30,0,4,3,26,0,32,0,2,18,4,7,34,0,16,0,2,0,44,5,2,3,8,0,66,7,4,3,2,5,32,0,16,9,24,0,42,0,8,39
%N A326067 a(n) = sigma(n) - sigma(A032742(n)) - n, where A032742 gives the largest proper divisor of n, and sigma is the sum of divisors of n.
%H A326067 Antti Karttunen, <a href="/A326067/b326067.txt">Table of n, a(n) for n = 1..16384</a>
%H A326067 Antti Karttunen, <a href="/A326067/a326067.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%H A326067 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>.
%F A326067 a(n) = A326066(n) - n = A000203(n) - A000203(A032742(n)) - n.
%F A326067 a(n) = A326068(n) - A033879(n).
%F A326067 a(p^k) = 0 for all primes and all exponents k >= 1.
%F A326067 Sum_{k=1..n} a(k) ~ ((zeta(2) * (1 - c) - 1)/2) * n^2, where c is defined in the corresponding formula in A326065. . - _Amiram Eldar_, Dec 21 2024
%o A326067 (PARI)
%o A326067 A032742(n) = if(1==n,n,n/vecmin(factor(n)[,1]));
%o A326067 A326066(n) = (sigma(n) - sigma(A032742(n)));
%o A326067 A326067(n) = (A326066(n) - n);
%Y A326067 Cf. A000203, A013661, A032742, A033879, A246655 (positions of zeros), A326065, A326066, A326068, A326069.
%K A326067 sign
%O A326067 1,6
%A A326067 _Antti Karttunen_, Jun 06 2019