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.

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, 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, 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

Offset: 1

Author

Antti Karttunen, Jun 06 2019

Keywords

• nonn

Comments

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.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A035316, A285309, A326058, A326059.

Cf. also A009194, A325385, A325813, A325975, A326046, A326047, A326048, A326056, A326057, A326062.

Programs

PARI

A035316(n) = sumdiv(n,d,issquare(d)*d);
A326058(n) = (n-A035316(n));
A285309(n) = sumdiv(n,d,(!issquare(d))*d);
A326059(n) = (A285309(n)-n);
A326060(n) = gcd(A326058(n), A326059(n));

Formula

a(n) = gcd(A326058(n), A326059(n)) = gcd(n-A035316(n), A285309(n)-n).