A092911 Numbers all of whose divisors can be formed using their digits. Divisor digits are a subset of the digits of the number.

1, 11, 13, 17, 19, 31, 41, 61, 71, 101, 103, 107, 109, 113, 121, 125, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 241, 251, 271, 281, 311, 313, 317, 331, 401, 419, 421, 431, 461, 491, 521, 541, 571

Offset: 1

Author

Amarnath Murthy, Mar 14 2004

Keywords

• base
• nonn

Comments

All primes containing 1 are members.

Sequence is a subsequence of A011531. The first nonprime terms of the sequence are 1, 121, 125, 1207, 1255, 1379, 10201, 10379, 11009, 11209, 12419, 12709, 12755, ... - R. J. Mathar, Jul 26 2007

Examples

			131 is a term. 143 is not a term as the divisor 11 contains two 1's.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A011531, A062634, A092912.

Programs

Maple

isA092911 := proc(n) local digs, digsleft,divs, d,i,j ; digs := convert(n,base,10) ; divs := numtheory[divisors](n) ; for i from 1 to nops(divs) do digsleft := digs ; d := convert(op(i,divs),base,10) ; for j in d do if member(j,digsleft,'jposit') then digsleft := subsop(jposit=NULL,digsleft) ; else RETURN(false) ; fi ; od ; od ; RETURN(true) ; end: for n from 1 to 600 do if isA092911(n) then printf("%d, ",n) ; fi ; od ; # R. J. Mathar, Jul 26 2007

Mathematica

subQ[s1_, s2_] := AllTrue[Count[s1, #] & /@ (First /@ (t = Tally[s2])) - Last /@ t, # >= 0 &]; digQ[n1_, n2_] := subQ[IntegerDigits[n1], IntegerDigits[n2]]; seqQ[n_] := AllTrue[Most@Divisors[n], digQ[n, #] &]; Select[Range[600], seqQ] (* Amiram Eldar, Nov 12 2020 *)

Python

from sympy import divisors
from collections import Counter
def ok(n):
  ncounts = Counter(str(n))
  for d in divisors(n)[:-1]:
    divcounts = Counter(str(d))
    if any(ncounts[c] < divcounts[c] for c in divcounts): return False
  return True
print(list(filter(ok, range(1, 630)))) # Michael S. Branicky, May 08 2021

Extensions

Corrected and extended by R. J. Mathar, Jul 26 2007