A072227 - OEIS

%I #10 Sep 04 2023 16:34:34

%S 1,2,3,4,5,6,7,8,9,11,13,17,19,22,23,26,27,29,31,33,37,39,41,43,44,46,

%T 47,53,55,59,61,62,66,67,69,71,73,77,79,82,83,86,88,89,93,97,99,101,

%U 103,107,109,113,121,127,131,137,139,143,149,151,157,163,167,169,173

%N Numbers n such that reverse(d) divides reverse(n) for all divisors d of n.

%C All primes are in this sequence, so a(n) << n log n. Does a(n) ~ n log n? That is, are composites of relative density 0 in this sequence? - _Charles R Greathouse IV_, Sep 12 2012

%H Charles R Greathouse IV, <a href="/A072227/b072227.txt">Table of n, a(n) for n = 1..10000</a>

%e The divisors of 187 are 1, 11, 17, 187, with reverses 1, 11, 71, 781 which all divide 781, the reverse of 187, so 187 is a term of the sequence.

%t rev[n_] := FromDigits[Reverse[IntegerDigits[n]]]; a = {}; Do[d = Map[rev, Divisors[n]]; l = Length[d]; e = rev[n]; r = True; For[i = 1, i <= l, i++, If[ ! IntegerQ[e/d[[i]]], r = False]]; If[r, a = Append[a, n]], {n, 1, 200}]; a

%t Select[Range[200],Union[Divisible[IntegerReverse[#],IntegerReverse/@Divisors[#]]]=={True}&] (* _Harvey P. Dale_, Sep 04 2023 *)

%o (PARI) rev(n)=eval(concat(vecextract(Vec(Str(n)), "-1..1")))

%o is(n)=my(r=rev(n));fordiv(n,d,if(r%rev(d),return(0)));1 \\ _Charles R Greathouse IV_, Sep 12 2012

%K base,easy,nonn

%O 1,2

%A _Joseph L. Pe_, Jul 05 2002