The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
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
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 22 06:48 EDT 2024. Contains 372743 sequences. (Running on oeis4.)