OFFSET
1,1
COMMENTS
The primes of the form (10^n - 1)/9 are terms (A004022).
A majority of numbers of the sequence are semiprimes (so with 3 proper divisors), except 11, 125, 2510, 16325, 21109, 72013, 126530, 132644, 163025, ... with the corresponding number of proper divisors 1, 3, 7, 5, 7, 7, 7, 5, 5, 5, 7, 7, ...
The even numbers of the sequence are rarer than the odd numbers: 2510, 12326, 17482, 105002, 123206, ...
All terms have a 1 in their decimal representation (A011531). - Michel Marcus, Feb 23 2017
The union of 11 and A237713. - R. J. Mathar, Mar 06 2017
EXAMPLE
16325 is in the sequence because the set of the digits is E = {1, 2, 3, 5, 6} and the proper divisors (or aliquot parts) of 16325 are 1, 5, 25, 653 and 3265 with the same set of digits.
MAPLE
with(numtheory):
for n from 1 to 200000 do:
z:=convert(n, base, 10):n0:=nops(z):lst1:={op(z), z[n0]}:
x:=divisors(n):n1:=nops(x):lst:={}:
for m from 1 to n1-1 do:
y:=convert(x[m], base, 10):n2:=nops(y):
lst2:={op(y), y[n2]}:lst:=lst union lst2
od:
if lst1=lst then
printf(`%d, `, n):
else
fi:
od:
MATHEMATICA
Select[Range[10^5], Function[k, Union@ Flatten@ Map[IntegerDigits, Most@ Divisors@ k] == Union@ IntegerDigits@ k]] (* Michael De Vlieger, Feb 25 2017 *)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Michel Lagneau, Feb 21 2017
STATUS
approved