A066480 Start of first run of exactly n consecutive integers with same number of anti-divisors.

5, 1, 19, 212, 231, 353755, 7077517, 841891, 96723128, 640141432, 83101215664, 3774913237385, 29738569261171

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

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