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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.

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

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OFFSET

1,3

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

FORMULA

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

PROG

(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));

CROSSREFS