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A242480
a(n) = (n*(n+1)/2) mod n + sigma(n) mod n + antisigma(n) mod n.
7
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
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
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, May 16 2014
STATUS
approved