A074749 Smallest difference between consecutive anti-divisors of n (ordered by size).

0, 0, 0, 0, 1, 0, 1, 2, 4, 1, 1, 3, 1, 1, 4, 8, 1, 1, 1, 5, 4, 1, 1, 9, 1, 1, 1, 2, 1, 8, 1, 2, 1, 1, 1, 16, 1, 1, 1, 6, 1, 1, 1, 5, 1, 1, 1, 13, 1, 1, 4, 1, 1, 8, 1, 13, 1, 1, 1, 1, 1, 1, 1, 40, 1, 3, 1, 1, 4, 1, 1, 2, 1, 1, 4, 1, 1, 1, 1, 4, 1, 1, 1, 5, 1, 1

Offset

1,8

Comments

See A066272 for definition of anti-divisor.

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Example

For n=13, anti-divisors={2,3,5,9}; differences={1,2,4}; a(13) = smallest difference = 1.

Mathematica

min[s_] := If[Length[s] > 0, Min[s], 0]; min /@ Differences /@ Table[Select[Range[2, n - 1], Abs[Mod[n, #] - #/2] < 1 &], {n, 100}] (* Amiram Eldar, Feb 03 2020 after Harvey P. Dale at A066272 *)

Prog

(PARI) A074749(n) = { my(pad=0, md=0); for(k=2, n, if((n%k) && (!((2*n)%k) || !((2*n-1)%k) || !((2*n+1)%k)), if(pad, md=if(md, min(k-pad, md), k-pad)); pad = k)); (md); }; \\ Antti Karttunen, Jan 15 2025

Crossrefs

Cf. A066272, A130799.

Sequence in context: A186520 A158570 A295224 * A194524 A117136 A362142

Adjacent sequences: A074746 A074747 A074748 * A074750 A074751 A074752

Keyword

nonn

Author

Jason Earls, Sep 06 2002

Extensions

More terms from Amiram Eldar, Feb 03 2020

Status

approved