A154585 - OEIS

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A154585

a(n) = abs(Sum_{k=1..n} (-1)^k * (n-k+1 mod k)).

0, 1, 1, 0, 1, 2, 4, 0, 3, 4, 5, 4, 1, 10, 4, 3, 1, 2, 9, 2, 11, 12, 17, 11, 0, 13, 0, 1, 6, 7, 23, 8, 7, 20, 10, 9, 8, 25, 14, 13, 4, 3, 20, 13, 34, 35, 34, 26, 8, 13, 6, 5, 8, 25, 24, 1, 26, 27, 34, 33, 4, 37, 25, 6, 11, 12, 11, 16, 37, 38, 60, 59, 24, 25, 0, 19, 40, 41, 54, 14, 25, 26, 51

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OFFSET

1,6

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

EXAMPLE

a(5) = -(5 mod 1)+(4 mod 2)-(3 mod 3)+(2 mod 4)-(1 mod 5) = -0+0-0+2-1 = 1.

MAPLE

P:=proc(i) local a, n; for n from 1 by 1 to i do a:=abs(sum('(-1)^k*((n-k+1) mod k)', 'k'=1..n)); print(a); od; end: P(100);

MATHEMATICA

a[n_] := Abs @ Sum[(-1)^k * Mod[n - k + 1, k], {k, 1, n}]; Array[a, 100] (* Amiram Eldar, Sep 18 2021 *)

PROG