OFFSET
1,1
COMMENTS
There are infinitely many numbers in this sequence, since the growth of powers of small primes far outpaces the growth of their digits when concatenated.
First differs from A195330 at 320 which is a term there but not here.
LINKS
Haines Hoag, Table of n, a(n) for n = 1..20000
EXAMPLE
32 is a term since 32=2^5 and 25<32.
1152 is a term since 1152=2^7*3^2 and 27*32=864, and 864<1152.
MATHEMATICA
f[p_, e_] := 10^IntegerLength[e]*p + e; q[1] = False; q[k_] := Times @@ f @@@ FactorInteger[k] < k; Select[Range[3200], q] (* Amiram Eldar, Sep 26 2024 *)
PROG
(Python)
from math import prod
from sympy import factorint
def ok(n): return prod(int(str(p)+str(e)) for p, e in factorint(n).items()) < n
print([k for k in range(1, 3200) if ok(k)]) # Michael S. Branicky, Sep 27 2024
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Haines Hoag, Sep 17 2024
STATUS
approved