login
This site is supported by donations 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

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: A095016 A160684 A176045 * 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

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 17 00:08 EST 2019. Contains 329209 sequences. (Running on oeis4.)