A239876 Partial sums of A229110, where A229110(n) = antisigma(n) mod n = A024816(n) mod n.

0, 0, 2, 5, 9, 12, 18, 23, 28, 35, 45, 47, 59, 70, 76, 85, 101, 107, 125, 133, 143, 162, 184, 184, 203, 226, 240, 254, 282, 285, 315, 332, 350, 381, 403, 438, 474, 509, 531, 541, 581, 590, 632, 658, 670, 713, 759, 803, 844, 876, 906, 938, 990, 1005, 1043, 1063

Offset

1,3

Comments

Antisigma(n) = A024816(n) = sum of non-divisors of n.

See A239877 - values of n for which a(n) / n is integer.

Links

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

Formula

a(n) = Sum_{k = 1...n} antisigma(k) mod k = Sum_{k = 1...n} A229110(k).

a(n) = a(n-1) for numbers n from A159907 if there are no odd multiply perfect numbers (A007691).

Mathematica

Accumulate[Table[Mod[Total[Complement[Range[n], Divisors[n]]], n], {n, 60}]] (* Harvey P. Dale, Jul 05 2024 *)

Prog

(Magma)[&+[(k*(k+1)div 2 - SumOfDivisors (k)) mod k: k in [1..n]]: n in [1..1000]]

Crossrefs

Cf. A024816, A229110, A239877.

Sequence in context: A034806 A226822 A034307 * A070828 A112988 A218706

Adjacent sequences: A239873 A239874 A239875 * A239877 A239878 A239879

Keyword

nonn

Author

Jaroslav Krizek, Mar 29 2014

Status

approved