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A239868
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Sum of sigma(i) mod i for i from 1 to n.
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2
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0, 1, 2, 5, 6, 6, 7, 14, 18, 26, 27, 31, 32, 42, 51, 66, 67, 70, 71, 73, 84, 98, 99, 111, 117, 133, 146, 146, 147, 159, 160, 191, 206, 226, 239, 258, 259, 281, 298, 308, 309, 321, 322, 362, 395, 421, 422, 450, 458, 501, 522, 568, 569, 581, 598, 606, 629, 661
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OFFSET
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1,3
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LINKS
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FORMULA
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a(n) = Sum_{k = 1...n} sigma(k) mod k = Sum_{k = 1...n} A054024(k).
a(n) = a(n - 1) for multiply-perfect numbers n (A007691).
a(p) = a(p - 1) + 1 for prime p.
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EXAMPLE
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a(3) = 2 because sigma(3) = 4 = 1 mod 3 and a(2) + 1 = 2.
a(4) = 5 because sigma(4) = 7 = 3 mod 4 and a(3) + 3 = 5.
a(5) = 6 because sigma(5) = 6 = 1 mod 5 and a(4) + 1 = 6.
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MATHEMATICA
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Table[Sum[Mod[DivisorSigma[1, i], i], {i, n}], {n, 60}] (* Alonso del Arte, Mar 30 2014 *)
Accumulate[Table[Mod[DivisorSigma[1, n], n], {n, 60}]] (* Harvey P. Dale, Jun 06 2021 *)
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PROG
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(Magma) [&+[SumOfDivisors (k) mod k: k in [1..n]]: n in [1..1000]]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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