A242480 a(n) = (n*(n+1)/2) mod n + sigma(n) mod n + antisigma(n) mod n.

0, 2, 3, 8, 5, 6, 7, 16, 9, 20, 11, 12, 13, 28, 15, 32, 17, 18, 19, 20, 21, 44, 23, 24, 25, 52, 27, 28, 29, 30, 31, 64, 33, 68, 35, 72, 37, 76, 39, 40, 41, 42, 43, 88, 45, 92, 47, 96, 49, 100, 51, 104, 53, 54, 55, 56, 57, 116, 59, 120, 61, 124, 63, 128, 65, 66

Offset

1,2

Comments

a(n) / n = 1 for numbers n from A242482, a(n) / n = 2 for numbers n from A242483.

If there are any odd multiply-perfect numbers n > 1 then a(n) = 0.

Possible values of a(n) in increasing order = A242485. Numbers m such that a(n) = m has no solution = A242486.

Links

Jaroslav Krizek, Table of n, a(n) for n = 1..10000

Formula

a(n) = A142150(n) + A054024(n) + A229110(n) = (A000217(n) mod n) + (A000203(n) mod n) + (A024816(n) mod n).

a(n) = A242481(n) * n.

Example

a(8) = (8*(8+1)/2) mod 8 + sigma(8) mod 8 + antisigma(8) mod 8 = 36 mod 8 + 15 mod 8 + 21 mod 8 = 4 + 7 + 5 = 16.

Prog

(Magma) [((n*(n+1)div 2 mod n + SumOfDivisors(n) mod n + (n*(n+1)div 2-SumOfDivisors(n)) mod n)): n in [1..1000]]

Crossrefs

Cf. A242481, A242482, A242483, A242484, A242485, A242486.

Sequence in context: A135874 A138682 A065632 * A175068 A355264 A157488

Adjacent sequences: A242477 A242478 A242479 * A242481 A242482 A242483

Keyword

nonn

Author

Jaroslav Krizek, May 16 2014

Status

approved