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A092911
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Numbers all of whose divisors can be formed using their digits. Divisor digits are a subset of the digits of the number.
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5
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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
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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EXAMPLE
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131 is a term. 143 is not a term as the divisor 11 contains two 1's.
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MAPLE
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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
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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