A073638 Number of anti-divisors of n (A066272) sets a record.

1, 3, 5, 7, 13, 17, 32, 38, 67, 137, 203, 247, 472, 578, 682, 787, 1463, 2047, 2363, 3465, 5197, 5198, 8662, 13513, 15593, 22522, 22523, 29452, 60638, 67567, 67568, 98753, 112612, 157658, 202702, 337837, 337838, 427927, 713212, 788287, 788288, 1013512

Offset

1,2

Comments

antid(n) > antid(k) for all k < n.

Note that several of these come in pairs, i.e., 5197 & 5198, 22522 & 22523, 67567 & 67568, 337837 & 337838, 788287 & 788288, 1013512 & 1013513 and 1914412 & 1914413 to name a few. See A093071 for more. - Robert G. Wilson v, Mar 17 2004

See A066272 for definition of anti-divisor.

Links

Donovan Johnson, Table of n, a(n) for n = 1..117 (terms < 5*10^11)

Jon Perry, Anti-divisors.

Jon Perry, The Anti-divisor [Cached copy]

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

Mathematica

antid[n_] := Select[ Union[ Join[ Select[ Divisors[2n - 1], OddQ[ # ] && # != 1 &], Select[ Divisors[2n + 1], OddQ[ # ] && # != 1 & ], 2n/Select[ Divisors[ 2n], OddQ[ # ] && # != 1 &]]], # < n &]; a = 0; Do[b = Length[ antid[ n]]; If[b > a, Print[n]; a = b], {n, 1, 1013513}] (* Robert G. Wilson v, Mar 17 2004 *)

Crossrefs

Sequence in context: A182981 A234388 A003424 * A066464 A062324 A194829

Adjacent sequences: A073635 A073636 A073637 * A073639 A073640 A073641

Keyword

nonn

Author

Jason Earls, Sep 01 2002

Extensions

More terms from Robert G. Wilson v, Mar 17 2004

Status

approved