A192276 Numbers n such that the number of anti-divisors of n divides n.

3, 4, 6, 8, 12, 15, 16, 21, 24, 25, 30, 35, 36, 40, 48, 51, 54, 55, 60, 63, 64, 65, 69, 70, 72, 75, 80, 84, 90, 96, 100, 112, 114, 120, 125, 126, 133, 140, 141, 143, 147, 155, 156, 160, 161, 171, 174, 180, 189, 190, 200, 205, 207, 210, 216, 220, 231, 240

Offset

1,1

Comments

Like A033950 but using anti-divisors.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Example

There are 3 anti-divisors of 30: 4, 12, 10; 3 divides 30, so 30 is in the sequence.

Maple

with(numtheory);
P:=proc(i)
local a, b, k, n;
for n from 3 by 1 to i do
   a:={};
   for k from 2 to n-1 do if abs((n mod k)- k/2) < 1 then a:=a union {k}; fi; od;
   b:=nops(a);
   if trunc(n/b)=n/b then print(n); fi;
od;
end:
P(10000);

Mathematica

Select[Range[3, 400], Function[n, Mod[n, Length@Select[Range[2, n - 1], Abs[Mod[n, #] - #/2] < 1 &]] == 0]] (* Olivier Gérard, Jul 05 2011 *)

Prog

(Magma) Antidivisors:=func< n | [ d: d in [1..n-1] | n mod d ne 0 and ((IsEven(d) and 2*n mod d eq 0) or (IsOdd(d) and ((2*n-1) mod d eq 0 or (2*n+1) mod d eq 0))) ] >; [ n: n in [3..10^4] | IsDivisibleBy(n, #Antidivisors(n)) ];  // Bruno Berselli, Jul 06 2011
(Python)
[n for n in range(3, 10**5) if not n % len([d for d in range(2, n) if n%d and 2*n%d in [d-1, 0, 1]])] # Chai Wah Wu, Aug 08 2014

Crossrefs

Cf. A033950, A066272.

Sequence in context: A320592 A225531 A129295 * A049305 A147606 A279083

Adjacent sequences: A192273 A192274 A192275 * A192277 A192278 A192279

Keyword

nonn

Author

Paolo P. Lava, Jul 05 2011

Status

approved