A255733 Numbers x such that the sum of remainders of x mod k, where k runs through the anti-divisors of x, divides x.

3, 4, 6, 12, 26, 96, 137, 946, 1053, 2943, 6874, 17386, 39182, 60504, 114254, 167786, 393216, 497134, 645354, 5250086, 27914146, 448005874, 505235234, 708458286, 3238952914, 71258123714

Offset

1,1

Comments

For a(7) = 137, a(9) = 1053 and a(10) = 2943 the ratio is 1.

a(27) > 10^11. - Hiroaki Yamanouchi, Mar 17 2015

Links

Table of n, a(n) for n=1..26.

Example

The anti-divisors of 26 are 3, 4, 17.
26 mod 3 = 2; 26 mod 4 = 2; 26 mod 17 = 9; 2 + 2 + 9 = 13 and 26 / 13 = 2.

Maple

with(numtheory): P:=proc(q) local a, k, n;
for n from 3 to q do a:=0;
for k from 2 to n-1 do if abs((n mod k)-k/2)<1 then a:=a+(n mod k);
fi; od; if type(n/a, integer) then print(n); fi; od; end: P(10^6);

Mathematica

f[n_] := Block[{ad}, ad[x_] := Cases[Range[2, x - 1], _?(Abs[Mod[x, #] - #/2] < 1 &)]; Plus @@ (Mod[n, #] & /@ ad@ n)]; Select[Range@ 5000, Mod[#, f@ #] == 0 &] (* Michael De Vlieger, Mar 05 2015 *)

Prog

(PARI) isok(n) = (n % sum(k=2, n-1, (n % k)*(abs((n % k)-k/2) < 1))) == 0; \\ Michel Marcus, Mar 06 2015

Crossrefs

Cf. A066272.

Sequence in context: A160684 A176045 A350299 * A137333 A006719 A202855

Adjacent sequences: A255730 A255731 A255732 * A255734 A255735 A255736

Keyword

nonn,more

Author

Paolo P. Lava, Mar 05 2015

Extensions

a(13)-a(26) from Hiroaki Yamanouchi, Mar 17 2015

Status

approved