A237713 Composite numbers n such that the distinct digits in n and the distinct digits in the proper divisors of n are the same.

125, 1255, 2510, 11009, 11099, 11255, 11379, 12326, 12955, 14379, 14397, 15033, 15303, 16325, 17482, 21109, 25105, 31007, 31503, 33011, 35213, 37127, 37921, 41303, 44011, 49319, 51367, 53491, 63013, 69413, 70319, 71057, 72013, 72517, 74341, 77011, 81767

Offset: 1

Author

Michel Lagneau, Feb 12 2014

Keywords

• nonn
• base

Comments

Since 1 is always a divisor of n, this is a subsequence of A011531. - Michel Marcus, Feb 12 2014

Examples

			125 is in the sequence because the proper divisors of 125 are {1, 5, 25} with the same digits as 125.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A032741, A035141.

See A282755 for a variant.

Programs

Mathematica

Pn[n_]:=Sort[DeleteDuplicates[Flatten[IntegerDigits[Take[Divisors[n],DivisorSigma[0,n]-1]]]]];Fn[n_]:=Sort[DeleteDuplicates[IntegerDigits[n]]];lst={};Do[If[!PrimeQ[n]&&Pn[n]===Fn[n],AppendTo[lst,n]],{n,2,10^5}];lst
Select[Range[10^5], ! PrimeQ@# && Union@ IntegerDigits@ # == Union @@ IntegerDigits /@ Most@ Divisors@ # &] (* Giovanni Resta, Feb 12 2014 *)

PARI

isok(n) = { my(digs = []); fordiv(n, d, if (d != n, digs = concat(digs, digits(d)))); (n != 1) && !isprime(n) && vecsort(digs,,8) == vecsort(digits(n),,8);} \\ Michel Marcus, Feb 12 2014