A069656 Perfect powers that can be permuted into another perfect power (in base 10).

125, 144, 169, 196, 243, 256, 324, 441, 512, 625, 961, 1024, 1089, 1296, 1369, 1728, 1764, 1936, 2187, 2197, 2401, 2916, 4096, 4761, 7921, 9216, 9261, 9604, 9801, 10201, 10404, 10609, 11236, 11664, 12100, 12544, 12769, 13689, 14400, 14884, 15129, 16384, 16641, 16807

Offset: 1

Author

Amarnath Murthy, Apr 04 2002

Keywords

• nonn
• base

Examples

			1024 = 2^10 and a digit permutation gives 2401 = 7^4.
1369 = 37^2 and a digit permutation gives 1936 = 44^2
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001597.

Programs

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 }
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

Extensions

Corrected and extended by Bodo Zinser, Apr 03 2005

Better definition from Jon Wild, Aug 20 2020

More terms from David A. Corneth, Aug 20 2020