login
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.
15
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
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));
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jun 06 2019
STATUS
approved