A069656 - OEIS

%I #23 Aug 24 2020 22:30:34

%S 125,144,169,196,243,256,324,441,512,625,961,1024,1089,1296,1369,1728,

%T 1764,1936,2187,2197,2401,2916,4096,4761,7921,9216,9261,9604,9801,

%U 10201,10404,10609,11236,11664,12100,12544,12769,13689,14400,14884,15129,16384,16641,16807

%N Perfect powers that can be permuted into another perfect power (in base 10).

%H David A. Corneth, <a href="/A069656/b069656.txt">Table of n, a(n) for n = 1..10000</a>

%e 1024 = 2^10 and a digit permutation gives 2401 = 7^4.

%e 1369 = 37^2 and a digit permutation gives 1936 = 44^2

%o (PARI) upto(n) = {l = List(); res = List(); for(i = 2, sqrtint(n), if(!ispower(i), for(j = 2, logint(n, i), c = i^j; listput(l, [freqdigits(c), c]); ) ) ); listsort(l, 1); for(i = 1, #l - 1, if(l[i][1] == l[i+1][1], k = i+1; while(k <= #l && l[i][1] == l[k][1], k++; ); for(j = i, k-1, listput(res, l[j][2]) ); ) ); listsort(res, 1); res }

%o addhelp(freqdigits, "Gives a vector that lists for every digit how often it occurs.") freqdigits(n) = {my(v=vector(10), d=digits(n)); for(i=1,#d,v[d[i]+1]++);v } \\ _David A. Corneth_, Aug 20 2020

%Y Cf. A001597.

%K nonn,base

%O 1,1

%A _Amarnath Murthy_, Apr 04 2002

%E Corrected and extended by _Bodo Zinser_, Apr 03 2005

%E Better definition from _Jon Wild_, Aug 20 2020

%E More terms from _David A. Corneth_, Aug 20 2020