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

1,3

Links

Jaroslav Krizek, Table of n, a(n) for n = 1..1000

Formula

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.

Example

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.

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 *)

Prog

(Magma) [&+[SumOfDivisors (k) mod k: k in [1..n]]: n in [1..1000]]

Crossrefs

Cf. A000203, A054024, A239869 (values of n for which a(n) / n is integer).

Sequence in context: A233588 A113975 A035585 * A159076 A273237 A278084

Adjacent sequences: A239865 A239866 A239867 * A239869 A239870 A239871

Keyword

nonn

Author

Jaroslav Krizek, Mar 28 2014

Status

approved