A390451 Numbers k such that the concatenation of a permutation of its divisors is prime.

3, 4, 7, 9, 12, 13, 16, 19, 21, 25, 27, 28, 31, 36, 37, 39, 43, 48, 52, 57, 63, 64, 67, 73, 75, 76, 79, 81, 84, 91, 93, 97, 100, 103, 108, 109, 111, 112, 117, 121, 124, 129, 133, 144, 148, 151, 156, 157, 163, 171, 172, 175, 181, 183, 189, 192, 193, 201, 208, 211, 217, 219, 223

Offset

1,1

Links

Michael S. Branicky, Table of n, a(n) for n = 1..2461

Michael S. Branicky, Table of n, a(n), associated_prime(n) for n = 1..2461

Michael S. Branicky, Python program for OEIS A390451

Example

k   Prime from reordered divisor string
3   13
4   241
7   17
9   139
12  1241263
13  113
16  248161
19  191

Mathematica

okQ[k_]:=AnyTrue[FromDigits/@Flatten/@IntegerDigits/@Permutations[Divisors[k]], PrimeQ]; Select[Range[43], okQ] (* James C. McMahon, Nov 11 2025 *)

Prog

(Python) # see links for a version suitable for producing b-file and a-file
from itertools import permutations
from sympy import divisors, isprime
def ok(n):
    d = list(map(str, divisors(n)))
    return n > 2 and sum(map(int, "".join(d)))%3 and any(isprime(int("".join(p))) for p in permutations(d))
print([k for k in range(190) if ok(k)]) # Michael S. Branicky, Nov 06 2025

Crossrefs

Cf. A003136, A037278, A176554, A176555, A176553 (a subsequence without the first term 1).

Sequence in context: A034022 A329963 A198772 * A185256 A070992 A246514

Adjacent sequences: A390448 A390449 A390450 * A390452 A390453 A390454

Keyword

nonn,base

Author

Jean-Marc Rebert, Nov 06 2025

Extensions

a(40) onward from Michael S. Branicky, Nov 06 2025

Status

approved