A161860 Squares which are anagrams of cubes.

1, 64, 729, 1296, 2916, 4096, 7921, 9216, 9604, 13689, 15129, 15625, 25921, 46656, 66564, 117649, 119025, 125316, 147456, 159201, 237169, 257049, 260100, 262144, 292681, 300304, 338724, 447561, 497025, 531441, 546121, 611524, 687241, 725904

Offset

1,2

Comments

13689 is a term because it is a square (117^2) and 19683 (an anagram of 13689) is a cube (27^3).

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..388 from Harvey P. Dale)

Mathematica

sacQ[n_]:=Module[{len=IntegerLength[n], trms=FromDigits/@Permutations[ IntegerDigits[ n]]}, trms=Select[ trms, IntegerLength[#]==len&]; AnyTrue[ trms, IntegerQ[Surd[#, 3]]&]]; Select[Range[900]^2, sacQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 03 2019 *)

Prog

(Python)
from itertools import count, takewhile
def hash(n): return "".join(sorted(str(n)))
def aupto_digits(d):
    cubes   = takewhile(lambda x:x<10**d, (i**3 for i in count(1)))
    squares = takewhile(lambda x:x<10**d, (i**2 for i in count(1)))
    C = set(map(hash, cubes))
    return [s for s in squares if hash(s) in C]
print(aupto_digits(6)) # Michael S. Branicky, Feb 18 2024

Crossrefs

Cf. A000290 (squares), A000578 (cubes).

Sequence in context: A164337 A354178 A367803 * A195249 A223953 A224137

Adjacent sequences: A161857 A161858 A161859 * A161861 A161862 A161863

Keyword

nonn,base

Author

Claudio Meller, Jun 20 2009

Status

approved