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

1,2

Comments

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

Links

Table of n, a(n) for n=1..15.

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 *)

Prog

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

Crossrefs

Cf. A001597, A009996, A028822, A062826.

Sequence in context: A306916 A387201 A385517 * A385516 A162752 A076966

Adjacent sequences: A355060 A355061 A355062 * A355064 A355065 A355066

Keyword

nonn,base,more

Author

Jon E. Schoenfield, Jun 16 2022

Status

approved