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URL: https://oeis.org/A255733

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A255733
Numbers x such that the sum of remainders of x mod k, where k runs through the anti-divisors of x, divides x.
0
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
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
KEYWORD
nonn,more
AUTHOR
Paolo P. Lava, Mar 05 2015
EXTENSIONS
a(13)-a(26) from Hiroaki Yamanouchi, Mar 17 2015
STATUS
approved