A159078 Number of perfect powers with distinct digits in base n.

1, 1, 9, 8, 25, 50, 88, 297, 657, 1418, 3212, 8662, 24185, 64103, 183718

Offset: 2

Author

Johan Särnbratt, Apr 04 2009

Keywords

• nonn
• base
• more

Examples

			The 8 powers with unique digits in base 5 are 1, 4, 8, 9, 16, 27, 144, and 576; in base 5 these are 1, 4, 13, 14, 31, 102, 1304, and 4301.
		

Crossrefs

Cf. A075309

Programs

PARI

okdigs(digs) = {for (i = 1, #digs-1, for (j = i+1, #digs, if (digs[j] == digs[i], return (0);););); return (1);}
a(n) = {b = n; sols = Set([1]); vmax = b^b; pmax = ceil(log(vmax)/log(2)); for (p = 2, pmax, i = 2; while ((iep = i^p) < vmax, if (okdigs(digits(iep, b)), sols = Set(concat(sols, iep));); i++;);); #sols;} \\ Michel Marcus, Aug 19 2013

Extensions

a(11) - a(16) from Johan Särnbratt, Apr 21 2009