A243363 Numbers with divisors containing all the digits 0-9 and each digit appears exactly once (in base 10).

203457869, 203465789, 203465897, 203468579, 203475869, 203478659, 203485697, 203485769, 203495867, 203548967, 203564897, 203568947, 203574689, 203584679, 203584769, 203594687, 203596847, 203598467, 203645879, 203645987, 203648957, 203654987, 203659487, 203674589

Offset

1,1

Comments

Primes made up of distinct digits except 1.

There are no composite numbers with divisors containing all the digits 0-9 and each digit appears exactly once.

Subsequence of A029743 (primes with distinct digits).

Numbers n such that A243360(n) = 9876543210.

Sequence contains 19558 terms, the last term is a(19558) = 987625403.

Links

Michael S. Branicky, Table of n, a(n) for n = 1..19558 (full sequence)

Mathematica

Select[Range[203*10^6, 204*10^6], Sort[Flatten[IntegerDigits/@ Divisors[#]]] == Range[0, 9]&] (* Harvey P. Dale, Aug 22 2016 *)

Prog

(Magma) [n: n in [1..1000000] | Seqint(Sort(&cat[(Intseq(k)): k in Divisors(n)])) eq 9876543210]
(Python) # generates entire sequence
from sympy import isprime
from itertools import permutations as perms
dist = (int("".join(p)) for p in perms("023456789", 9) if p[0] != "0")
afull = [k for k in dist if isprime(k)]
print(afull[:24]) # Michael S. Branicky, Aug 04 2022

Crossrefs

Cf. A037278, A176558, A243360, A243361, A243362, A243364.

Sequence in context: A358019 A015427 A078249 * A273094 A226079 A034641

Adjacent sequences: A243360 A243361 A243362 * A243364 A243365 A243366

Keyword

nonn,base,fini,full

Author

Jaroslav Krizek, Jun 04 2014

Status

approved