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A376254
Numbers k such that A376294(k) < k.
2
32, 64, 81, 121, 125, 128, 169, 243, 256, 289, 343, 361, 512, 529, 625, 729, 841, 864, 961, 972, 1024, 1152, 1250, 1296, 1331, 1369, 1458, 1536, 1600, 1681, 1728, 1849, 1875, 1944, 2000, 2025, 2048, 2187, 2197, 2209, 2304, 2401, 2500, 2560, 2592, 2662, 2744, 2809, 2916, 3087, 3125, 3136
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.
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
Sequence in context: A116318 A225722 A195330 * A122616 A174312 A255995
KEYWORD
nonn,base
AUTHOR
Haines Hoag, Sep 17 2024
STATUS
approved