A388007 a(n) = Sum_{j=1..A066272(n)} (A066417(n) mod d_j), where d_j are the antidivisors of n.

0, 0, 0, 0, 3, 0, 1, 5, 2, 4, 5, 8, 7, 8, 8, 5, 10, 7, 5, 11, 12, 7, 16, 9, 19, 7, 17, 18, 5, 16, 6, 32, 16, 9, 19, 8, 7, 37, 15, 10, 22, 34, 35, 12, 58, 38, 32, 43, 14, 27, 8, 52, 43, 20, 14, 29, 47, 34, 35, 56, 19, 45, 50, 4, 51, 58, 110, 40, 8, 30, 51, 50, 36

Offset

1,5

Links

Paolo P. Lava, Table of n, a(n) for n = 1..1000

Example

Antidivisors of 17 are 2, 3, 5, 7, 11, whose sum is 28.
Then, 28 mod 2 + 28 mod 3 + 28 mod 5 + 28 mod 7 + 28 mod 11 = 0 + 1 + 3 + 0 + 6 = 10.

Maple

P:=proc(q) local a, b, c, k, n; c:=[]; for n from 1 to q do a:=[]; for k from 2 to n-1 do
if abs((n mod k)-k/2)<1 then a:=[op(a), k]; fi; od; b:=add(k, k=a); c:=[op(c), add(b mod k, k=a)];
od; op(c); end: P(10^2);

Mathematica

Table[Function[{s, t}, Sum[Mod[t, s[[i]] ], {i, Length[s]}]] @@ {#, Total[#]} &@ Select[Range[2, n - 1], Abs[Mod[n, #] - #/2] < 1 &], {n, 73}] (* Michael De Vlieger, Oct 15 2025 *)

Prog

(PARI) isad(x, n) = if (n%x, if (x%2, !((2*n-1)%x) || !((2*n+1)%x), !((2*n)%x)));
adrow(n) = select(x->isad(x, n), [2..n-1]); \\ A130799
a(n) = my(v=adrow(n), s=vecsum(v)); sum(k=1, #v, s % v[k]); \\ Michel Marcus, Oct 15 2025
(Python)
from sympy.ntheory.factor_ import antidivisors
def a(n):
    ad = antidivisors(n)
    sad = sum(ad)
    return sum(sad%d for d in ad)
print([a(n) for n in range(1, 74)]) # Michael S. Branicky, Oct 18 2025

Crossrefs

Cf. A066272, A066417, A130799, A318996.

Cf. A389846 (fixed points).

Sequence in context: A346242 A020768 A246182 * A104544 A123880 A186363

Adjacent sequences: A388004 A388005 A388006 * A388008 A388009 A388010

Keyword

nonn,easy

Author

Paolo P. Lava, Oct 14 2025

Status

approved