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A192276 Numbers n such that the number of anti-divisors of n divides n. 1
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 (list; graph; refs; listen; history; text; internal format)
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 xrange(3, 10**5) if not n % len([d for d in xrange(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: A227956 A225531 A129295 * A049305 A147606 A279083

Adjacent sequences:  A192273 A192274 A192275 * A192277 A192278 A192279

KEYWORD

nonn

AUTHOR

Paolo P. Lava, Jul 05 2011

STATUS

approved

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Last modified September 26 15:27 EDT 2017. Contains 292531 sequences.