OFFSET
1,2
COMMENTS
Equivalently, A060763(n)=0.
Powers of 2 and factorials up to 7! are here.
For each k=1..A000005(a(n))-1 exists k' < A000005(a(n)) such that A193829(a(n),k) = A027750(a(n),k'). - Reinhard Zumkeller, Jun 25 2015
From Robert Israel, Jul 03 2017: (Start)
Also includes 3*2^k and 2*3^k for all k>= 1.
All terms except 1 are even. (End)
Conjecture: a(n) has the property that for each prime divisor p, p-1|a(n)/p. If this conjecture is true then terms can be searched by distinct prime divisors. - David A. Corneth, Jul 06 2017
The divisors of a(n) form a Brauer chain. See A079301 for the definition of a Brauer chain. - Zizheng Fang, Jan 30 2020
LINKS
Donovan Johnson, Table of n, a(n) for n = 1..750
EXAMPLE
For n = 12, divisors={1, 2, 3, 4, 6, 12}; differences={1, 1, 1, 2, 6}; every difference is a divisor, so 12 is in the sequence.
MAPLE
f:= proc(n) local D, L;
D:= numtheory:-divisors(n);
L:= sort(convert(D, list));
nops(convert(L[2..-1]-L[1..-2], set) minus D);
end proc:
select(f=0, [$1..1000]); # Robert Israel, Jul 03 2017
MATHEMATICA
test[n_ ] := Length[Complement[Drop[d=Divisors[n], 1]-Drop[d, -1], d]]==0; Select[Range[1, 1024], test]
(* Second program: *)
Select[Range[2^10], Function[n, AllTrue[Differences@ Divisors@ n, Divisible[n, #] &]]] (* Michael De Vlieger, Jul 12 2017 *)
PROG
(Haskell)
import Data.List (sort, nub); import Data.List.Ordered (subset)
a060765 n = a060765_list !! (n-1)
a060765_list = filter
(\x -> sort (nub $ a193829_row x) `subset` a027750_row' x) [1..]
-- Reinhard Zumkeller, Jun 25 2015
(PARI) isok(n)=my(d=divisors(n), v=vecsort(vector(#d-1, k, d[k+1]-d[k]), , 8)); #select(x->setsearch(d, x), v) == #v; \\ Michel Marcus, Jul 06 2017
(PARI) is(n)=my(t); fordiv(n, d, if(n%(d-t), return(0)); t=d); 1 \\ Charles R Greathouse IV, Jul 12 2017
(Magma) [k:k in [1..1025]| forall{i:i in [2..#Divisors(k)]|k mod (d[i]-d[i-1]) eq 0 where d is Divisors(k)}]; // Marius A. Burtea, Jan 30 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Apr 24 2001
EXTENSIONS
Edited by Dean Hickerson, Jan 22 2002
STATUS
approved