A355063 Perfect powers whose digits are in nonincreasing order and do not include 0.

1, 4, 8, 9, 32, 64, 81, 441, 841, 961, 7744, 7776, 8874441, 9853321, 999887641

Offset: 1

Author

Jon E. Schoenfield, Jun 16 2022

Keywords

• nonn
• base
• more

Comments

a(16) > 10^45 if it exists. - Michael S. Branicky, Jun 19 2022

Crossrefs

Cf. A001597, A009996, A028822, A062826.

Programs

Mathematica

perfectPowerQ[n_] := n==1||GCD @@ FactorInteger[n][[All, 2]] > 1; (* A001597 *) Select[Range[10^5], perfectPowerQ[#] && Max[Differences[d=IntegerDigits[#]]]<1 && Count[d,0]==0&] (* Stefano Spezia, Jul 01 2025 *)

PARI

isok(m) = if (ispower(m), my(d=digits(m)); vecmin(d) && (d == vecsort(d,,4))); \\ Michel Marcus, Jun 17 2022

Python

from sympy import perfect_power as pp
from itertools import count, islice, combinations_with_replacement as mc
def agen():
    yield 1
    for d in count(1):
        nd = (int("".join(m)) for m in mc("987654321", d))
        yield from sorted(filter(pp, nd))
print(list(islice(agen(), 14))) # Michael S. Branicky, Jun 16 2022