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A326060 a(n) = gcd(n-A035316(n), A285309(n)-n), where A035316 and A285309 give respectively the sums of square and nonsquare divisors of n.

%I A326060 #8 Jun 06 2019 21:59:00
%S A326060 1,1,2,1,4,5,6,1,1,1,10,1,12,1,2,1,16,1,18,1,10,1,22,1,1,5,1,23,28,1,
%T A326060 30,1,2,1,2,1,36,1,2,5,40,1,42,1,1,5,46,1,1,1,10,1,52,4,2,1,2,1,58,1,
%U A326060 60,1,1,1,2,1,66,1,2,1,70,1,72,1,1,1,2,1,78,1,1,1,82,1,2,5,2,1,88,2,10,1,2,1,2,15,96,1,1,1,100,1,102,1,2
%N A326060 a(n) = gcd(n-A035316(n), A285309(n)-n), where A035316 and A285309 give respectively the sums of square and nonsquare divisors of n.
%C A326060 Below 2^27 there are following numbers k such that a(k) is equal to A326059(k), and quotient A326058(k)/A326059(k) is odd: 6, 28, 496, 1625, 2057, 8128, 33550336, 107452235. The odd terms are factored as: 1625 = 5^3 * 13, 2057 = 11^2 * 17, 107452235 = 5 * 11^2 * 97 * 1831.
%H A326060 Antti Karttunen, <a href="/A326060/b326060.txt">Table of n, a(n) for n = 1..20000</a>
%F A326060 a(n) = gcd(A326058(n), A326059(n)) = gcd(n-A035316(n), A285309(n)-n).
%o A326060 (PARI)
%o A326060 A035316(n) = sumdiv(n,d,issquare(d)*d);
%o A326060 A326058(n) = (n-A035316(n));
%o A326060 A285309(n) = sumdiv(n,d,(!issquare(d))*d);
%o A326060 A326059(n) = (A285309(n)-n);
%o A326060 A326060(n) = gcd(A326058(n), A326059(n));
%Y A326060 Cf. A035316, A285309, A326058, A326059.
%Y A326060 Cf. also A009194, A325385, A325813, A325975, A326046, A326047, A326048, A326056, A326057, A326062.
%K A326060 nonn
%O A326060 1,3
%A A326060 _Antti Karttunen_, Jun 06 2019