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A120712
Numbers k with the property that the concatenation of the nontrivial divisors of k (i.e., excluding 1 and k) is a prime.
9
4, 6, 9, 21, 22, 25, 33, 39, 46, 49, 51, 54, 58, 78, 82, 93, 99, 111, 115, 121, 133, 141, 142, 147, 153, 154, 159, 162, 166, 169, 174, 177, 186, 187, 189, 201, 205, 219, 226, 235, 237, 247, 249, 253, 262, 267, 274, 286, 289, 291, 294, 301, 318
OFFSET
1,1
EXAMPLE
k | divisors | concatenation
---+----------------+--------------
4 | (1) 2 (4) | 2
6 | (1) 2, 3 (6) | 23
9 | (1) 3 (9) | 3
21 | (1) 3, 7 (21) | 37
22 | (1) 2, 11 (22) | 211
25 | (1) 5 (25) | 5
33 | (1) 3, 11 (33) | 311
39 | (1) 3, 13 (39) | 313
MAPLE
with(numtheory):
for k from 2 to 1000 do:
v0:=divisors(k):
nn:=nops(v0):
if nn > 2 then
v1:=[seq(v0[j], j=2..nn-1)]:
v2:=cat(seq(convert(v1[n], string), n=1..nops(v1))):
v3:=parse(v2):
if isprime(v3) = true then lprint(k, v3) fi:
fi:
MATHEMATICA
fQ[n_] := PrimeQ@ FromDigits@ Most@ Rest@ Divisors@ n; Select[ Range[2, 320], fQ]
PROG
(Python)
from sympy import divisors, isprime
def ok(n):
s = "".join(str(d) for d in divisors(n)[1:-1])
return s != "" and isprime(int(s))
print([k for k in range(319) if ok(k)]) # Michael S. Branicky, Oct 01 2024
KEYWORD
nonn,base
AUTHOR
Eric Angelini, Jul 19 2007
EXTENSIONS
Name edited by Michel Marcus, Mar 09 2023
STATUS
approved