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A066480 Start of first run of exactly n consecutive integers with same number of anti-divisors. 1
5, 1, 19, 212, 231, 353755, 7077517, 841891, 96723128, 640141432, 83101215664, 3774913237385, 29738569261171 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

See A066272 for definition of anti-divisor.

a(11) > 10^10. - Donovan Johnson, Apr 13 2013

LINKS

Table of n, a(n) for n=1..13.

Jon Perry, The Anti-Divisor

Jon Perry, The Anti-divisor [Cached copy]

Jon Perry, The Anti-divisor: Even More Anti-Divisors [Cached copy]

EXAMPLE

To illustrate the first 3 terms, here are the numbers of anti-divisors of the numbers 1 through 22: [0, 0, 1, 1, 2, 1, 3, 2, 2, 3, 3, 2, 4, 3, 3, 2, 5, 4, 3, 3, 3, 5] (see A066272). - N. J. A. Sloane, Oct 14 2019

MAPLE

with(numtheory); A066480:=proc(q) local a, b, c, j, k, n, t, v;

v:=array(1..1000); for j from 1 to 1000 do v[j]:=0; od; n:=1; a:=0;

while n<=q do

  b:=0; for k from 2 to n-1 do if abs((n mod k)-k/2)<1 then b:=b+1; fi; od;

  t:=n; c:=b;  while c=b do t:=t+1;

    b:=0; for k from 2 to t-1 do if abs((t mod k)-k/2)<1 then b:=b+1; fi; od; od;

  if t-n=a+1 then a:=t-n; print(n); j:=1;

   while v[a+j]>0 do a:=t-n+j; print(v[a]); j:=j+1; od;

  else if t-n>a+1 then if v[t-n]=0 then v[t-n]:=n; fi; fi; fi;

  n:=t; od; print(); end:

A066480(10^9); # Paolo P. Lava, Apr 16 2013

MATHEMATICA

a066272[n_] := Count[Range[2, n - 1], _?(Abs[Mod[n, #] - #/2] < 1 &)]

a[0] = 5;

a[n_] := For[i = 1, True, ++i, If[Equal @@ Table[a066272[j], {j, i, i + n}], Return[i]]]

a /@ Range[0, 4] (* Julien Kluge, Dec 03 2016 *)

PROG

(PARI) nbad(n) = #select(t->n%t && t<n, concat(concat(divisors(2*n-1), divisors(2*n+1)), 2*divisors(n))); \\ A066272

isok(k, n) = {my(nb=nbad(k)); if ((k>1) && nbad(k-1) == nb, return (0)); for (j=1, n-1, if (nbad(k+j) != nb, return(0)); ); nbad(k+n) != nb; }

a(n) = my(k=1); while (!isok(k, n), k++); k; \\ Michel Marcus, Oct 11 2019

CROSSREFS

Cf. A066272, A006558.

Sequence in context: A286232 A147437 A147369 * A136394 A145372 A145373

Adjacent sequences:  A066477 A066478 A066479 * A066481 A066482 A066483

KEYWORD

nonn,more

AUTHOR

Robert G. Wilson v, Jan 02 2002

EXTENSIONS

a(7) corrected and a(9)-a(10) from Donovan Johnson, Apr 13 2013

a(11)-a(12) from Jud McCranie, Oct 10 2019

a(11)-a(12) decremented by 1 by Michel Marcus, Oct 17 2019

a(13) from Jud McCranie, Oct 22 2019

STATUS

approved

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Last modified December 12 15:11 EST 2019. Contains 329960 sequences. (Running on oeis4.)