A355062 -id:A355062 - cp's OEIS frontend

A355060 Perfect powers whose digits are in strictly increasing order.

4, 8, 9, 16, 25, 27, 36, 49, 125, 128, 169, 256, 289, 1369, 13456, 13689, 134689

Offset: 1

Jon E. Schoenfield, Jun 16 2022

I.e., numbers of the form b^k with b > 1 and k > 1 in whose base-10 expansion each digit is greater than the previous digit.

Cf. A001597, A009993, A355062.

perfectPowerQ[n_] := GCD @@ FactorInteger[n][[All, 2]] > 1; (* A001597 *) Select[Range[135000], perfectPowerQ[#] && AllTrue[Differences[IntegerDigits[#]],Positive] &] (* Stefano Spezia, Jul 01 2025 *)

A385516 Perfect powers whose digits are in strictly decreasing order.

Original entry on oeis.org

1, 4, 8, 9, 32, 64, 81, 841, 961

Offset: 1

Stefano Spezia, Jul 01 2025

Cf. A001597, A009995, A355060, A355062, A355063, A385517.

perfectPowerQ[n_] := n==1 || GCD @@ FactorInteger[n][[All, 2]] > 1; (* A001597 *) Select[Range[1000], perfectPowerQ[#] && Max[Differences[IntegerDigits[#]]]<0 &]

A385517 Perfect powers whose digits are in nonincreasing order.

Original entry on oeis.org

1, 4, 8, 9, 32, 64, 81, 100, 400, 441, 841, 900, 961, 1000, 6400, 7744, 7776, 8000, 8100, 10000, 40000, 44100, 64000, 84100, 90000, 96100, 100000, 640000, 774400, 810000, 1000000, 3200000, 4000000, 4410000, 8000000, 8410000, 8874441, 9000000, 9610000, 9853321, 10000000

Offset: 1

Stefano Spezia, Jul 01 2025

Cf. A001597, A009995, A355060, A355062, A355063, A385516.

perfectPowerQ[n_] :=n==1 || GCD @@ FactorInteger[n][[All, 2]] > 1; (* A001597 *) Select[Range[10^6], perfectPowerQ[#] && Max[Differences[IntegerDigits[#]]]<1 &]

cp's OEIS Frontend

A355060 Perfect powers whose digits are in strictly increasing order.

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

A385516 Perfect powers whose digits are in strictly decreasing order.

Views

Author

Keywords

Crossrefs

Programs

Mathematica

A385517 Perfect powers whose digits are in nonincreasing order.

Views

Author

Keywords

Crossrefs

Programs

Mathematica