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

1,1

Comments

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

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A032741, A035141.

See A282755 for a variant.

Sequence in context: A204795 A352161 A243240 * A000526 A016971 A030082

Adjacent sequences: A237710 A237711 A237712 * A237714 A237715 A237716

Keyword

nonn,base

Author

Michel Lagneau, Feb 12 2014

Status

approved