A239868 Sum of sigma(i) mod i for i from 1 to n.
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
Offset: 1
Keywords
Examples
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.
Links
- Jaroslav Krizek, Table of n, a(n) for n = 1..1000
Programs
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Magma
[&+[SumOfDivisors (k) mod k: k in [1..n]]: n in [1..1000]]
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Mathematica
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 *) -
PARI
a(n) = sum(i=1, n, sigma(i) % i); \\ Michel Marcus, Jan 12 2025