A066478 Numbers having just twelve anti-divisors.

338, 450, 612, 722, 882, 1458, 1513, 1624, 1740, 1800, 2112, 2520, 2592, 2738, 3025, 3136, 3200, 3249, 3280, 3600, 3785, 3960, 4512, 5202, 5305, 5725, 6084, 6613, 7056, 7081, 7564, 8192, 8320, 8649, 9384, 9661, 10000, 10512, 10609, 12013, 12321

Offset

1,1

Comments

See A066272 for definition of anti-divisor.

Links

Table of n, a(n) for n=1..41.

Jon Perry, The Anti-Divisor

Jon Perry, The Anti-divisor [Cached copy]

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

Maple

A066478:= proc(q)
local k, n, t;
for n from 1 to q do
t:=0; for k from 2 to n-1 do if abs((n mod k)-k/2)<1 then t:=t+1; fi; od;
if t=12 then print(n); fi; od; end:
A066478(10^10); # Paolo P. Lava, Feb 22 2013

Mathematica

antid[n_] := Select[ Union[ Join[ Select[ Divisors[2n - 1], OddQ[ # ] && # != 1 & ], Select[ Divisors[2n + 1], OddQ[ # ] && # != 1 & ], 2n/Select[ Divisors[ 2*n], OddQ[ # ] && # != 1 &]]] }, # < n & ]]; Select[ Range[10^4], Length[ antid[ # ]] == 12 & ]
nd[n_]:=Count[Range[2, n-1], _?(Abs[Mod[n, #]-#/2]<1&)]; Select[Range[ 12500], nd[#]==12&] (* Harvey P. Dale, Jul 11 2012 *)

Crossrefs

Cf. A066272.

Sequence in context: A243483 A234625 A226539 * A261707 A202443 A188213

Adjacent sequences: A066475 A066476 A066477 * A066479 A066480 A066481

Keyword

nonn

Author

Robert G. Wilson v, Jan 02 2002

Status

approved