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

Author

Jaroslav Krizek, May 16 2014

Keywords

• nonn

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.

Examples

			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.
		

Links

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

Crossrefs

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

Programs

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]]

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.