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

1,3

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

Cf. A035316, A285309, A326058, A326059.

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

Sequence in context: A359900 A323955 A197011 * A321794 A075423 A144774

Adjacent sequences: A326057 A326058 A326059 * A326061 A326062 A326063

Keyword

nonn

Author

Antti Karttunen, Jun 06 2019

Status

approved