A066480 - OEIS

%I #44 Feb 23 2024 01:09:30

%S 5,1,19,212,231,353755,7077517,841891,96723128,640141432,83101215664,

%T 3774913237385,29738569261171

%N Start of first run of exactly n consecutive integers with same number of anti-divisors.

%C See A066272 for definition of anti-divisor.

%C a(11) > 10^10. - _Donovan Johnson_, Apr 13 2013

%H Jon Perry, <a href="http://www.users.globalnet.co.uk/~perry/maths/antidivisor.htm">The Anti-Divisor</a>

%H Jon Perry, <a href="/A066272/a066272a.html">The Anti-divisor</a> [Cached copy]

%H Jon Perry, <a href="/A066272/a066272.html">The Anti-divisor: Even More Anti-Divisors</a> [Cached copy]

%e 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

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

%t a[0] = 5;

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

%t a /@ Range[0, 4] (* _Julien Kluge_, Dec 03 2016 *)

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

%o 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;}

%o a(n) = my(k=1); while (!isok(k, n), k++); k; \\ _Michel Marcus_, Oct 11 2019

%Y Cf. A066272, A006558.

%K nonn,more

%O 1,1

%A _Robert G. Wilson v_, Jan 02 2002

%E a(7) corrected and a(9)-a(10) from _Donovan Johnson_, Apr 13 2013

%E a(11)-a(12) from _Jud McCranie_, Oct 10 2019

%E a(11)-a(12) decremented by 1 by _Michel Marcus_, Oct 17 2019

%E a(13) from _Jud McCranie_, Oct 22 2019