A285309 -id:A285309 - cp's OEIS frontend

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

Antti Karttunen, Jun 06 2019

nonn

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.

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

Cf. A035316, A285309, A326058, A326059.

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

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));

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

A326059 a(n) = A285309(n) - n, where A285309 gives the sum of nonsquare divisors of n.

Original entry on oeis.org

-1, 0, 0, -2, 0, 5, 0, 2, -6, 7, 0, 11, 0, 9, 8, -6, 0, 11, 0, 17, 10, 13, 0, 31, -20, 15, 3, 23, 0, 41, 0, 10, 14, 19, 12, 5, 0, 21, 16, 45, 0, 53, 0, 35, 23, 25, 0, 55, -42, 17, 20, 41, 0, 56, 16, 59, 22, 31, 0, 103, 0, 33, 31, -22, 18, 77, 0, 53, 26, 73, 0, 73, 0, 39, 23, 59, 18, 89, 0, 85, -51, 43, 0, 135, 22, 45, 32, 87, 0, 134, 20

Offset: 1

Antti Karttunen, Jun 06 2019

sign

Antti Karttunen, Table of n, a(n) for n = 1..16384
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Cf. A033879, A285309, A326058, A326060.

A285309(n) = sumdiv(n,d,(!issquare(d))*d);
A326059(n) = (A285309(n)-n);

a(n) = A285309(n) - n.

a(n) = A326058(n) - A033879(n).

A326053 Sum of all other divisors of n except the largest square divisor: a(n) = sigma(n) - A008833(n).

Original entry on oeis.org

0, 2, 3, 3, 5, 11, 7, 11, 4, 17, 11, 24, 13, 23, 23, 15, 17, 30, 19, 38, 31, 35, 23, 56, 6, 41, 31, 52, 29, 71, 31, 47, 47, 53, 47, 55, 37, 59, 55, 86, 41, 95, 43, 80, 69, 71, 47, 108, 8, 68, 71, 94, 53, 111, 71, 116, 79, 89, 59, 164, 61, 95, 95, 63, 83, 143, 67, 122, 95, 143, 71, 159, 73, 113, 99, 136, 95, 167, 79, 170, 40, 125, 83

Offset: 1

Antti Karttunen, Jun 05 2019

nonn

Antti Karttunen, Table of n, a(n) for n = 1..20000
Index entries for sequences related to sigma(n)

Cf. A000203, A008833, A285309, A326054, A326055.

A008833(n) = (n/core(n));
A326053(n) = (sigma(n)-A008833(n));

a(n) = A000203(n) - A008833(n).
a(n) = n + A326054(n).
a(n) >= A285309(n).

cp's OEIS Frontend

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.

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A326059 a(n) = A285309(n) - n, where A285309 gives the sum of nonsquare divisors of n.

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PARI

Formula

A326053 Sum of all other divisors of n except the largest square divisor: a(n) = sigma(n) - A008833(n).

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

Formula