A066472 Numbers having exactly six anti-divisors.

32, 49, 50, 60, 72, 81, 121, 128, 145, 180, 181, 196, 264, 288, 324, 361, 480, 529, 684, 685, 961, 1156, 1405, 2304, 2401, 2500, 2521, 2704, 2809, 4624, 4705, 5041, 5184, 7396, 8064, 8581, 9385, 10816, 11881, 13456, 14281, 25600, 26569, 27556, 34585

Offset

1,1

Comments

See A066272 for definition of anti-divisor.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..1000

Jon Perry, The Anti-Divisor [broken link; see below]

Jon Perry, The Anti-divisor [Cached copy]

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

Maple

A066472:= 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=6 then print(n); fi; od; end:
A066472(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[ # ]] == 6 & ]

Prog

(Python)
from sympy.ntheory.factor_ import antidivisor_count
A066472_list = [n for n in range(1, 10**5) if antidivisor_count(n) == 6] # Chai Wah Wu, Jul 25 2015

Crossrefs

Cf. A066272.

Sequence in context: A045023 A222300 A259770 * A140172 A259765 A256521

Adjacent sequences: A066469 A066470 A066471 * A066473 A066474 A066475

Keyword

nonn

Author

Robert G. Wilson v, Jan 02 2002

Status

approved