A188650 Fixed points of A188649: numbers divisible by the reverse of all their divisors.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 20, 22, 33, 40, 44, 55, 66, 77, 88, 99, 101, 110, 121, 131, 151, 181, 191, 202, 220, 242, 262, 303, 313, 353, 363, 373, 383, 393, 404, 440, 484, 505, 606, 626, 707, 727, 757, 787, 797, 808, 909, 919, 929, 939, 1010, 1111, 1331, 1441, 1661, 1991, 2020, 2222, 2662, 2882, 3333, 3443, 3883, 3993, 4040, 4444, 5555, 6666, 6886, 7777, 7997, 8888

Offset: 1

Author

Reinhard Zumkeller, Apr 11 2011

Keywords

• nonn
• base

Comments

A188649(a(n)) = a(n);

A002385 and A046376 are subsequences; subsequence of A002113.

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10700

Programs

Haskell

import Data.List (elemIndices)
a188650 n = a188650_list !! (n-1)
a188650_list =
   map succ $ elemIndices 0 $ zipWith (-) [1..] $ map a188649 [1..]

PARI

rev(n:int,B=10)=my(m=n%B);n\=B;while(n>0,m=m*B+n%B;n\=B);m
is(n)=fordiv(n,d,if(n%rev(d),return(0)));1 \\ Charles R Greathouse IV, Jul 14 2011

Python

from math import lcm
from sympy import divisors
def ok(n): return n == lcm(*(int(str(d)[::-1]) for d in divisors(n)))
print([k for k in range(1, 10000) if ok(k)]) # Michael S. Branicky, Sep 30 2022