A376254 Numbers k such that A376294(k) < k.
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
Examples
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.
Links
- Haines Hoag, Table of n, a(n) for n = 1..20000
Programs
-
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 *)
-
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
Comments