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

Author

Jaroslav Krizek, Jun 04 2014

Keywords

• nonn
• base
• fini
• full

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)

Crossrefs

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

Programs

Magma

[n: n in [1..203457879] | Seqint(Sort(&cat[(Intseq(k)): k in Divisors(n)])) eq 9876543210];

Mathematica

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

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