A075783 - OEIS

%I #24 Oct 02 2015 14:23:23

%S 1,4,8,9,27,36,81,100,121,125,144,169,196,216,225,243,324,400,441,484,

%T 512,529,900,961,1000,1331,1521,1681,2025,2304,2601,3364,3481,3600,

%U 3969,4489,4624,5776,5929,7225,7396,7569,7776,8000,8100,8649,8836,9025,10000

%N Additive perfect powers: sum-of-digits is also a perfect power.

%H Alois P. Heinz, <a href="/A075783/b075783.txt">Table of n, a(n) for n = 1..1000</a>

%e 121 is OK because sum-of-digits=1+2+1=4 is perfect power.

%t perfectPowerQ[n_] := n == 1 || GCD @@ FactorInteger[n][[All, 2]] > 1; Select[Range@ 10000, perfectPowerQ@ # && perfectPowerQ@ Total@ IntegerDigits@ # &] (* _Michael De Vlieger_, Oct 02 2015, after _Ant King_ at A001597 *)

%o (PARI) isok(n) = (n==1 || ispower(n)) && (sumdigits(n)==1 || ispower(sumdigits(n))) \\ _Dana Jacobsen_, Oct 01 2015

%o (Perl) use ntheory ":all"; my @seq = grep { ($_==1 || is_power($_)) && (sumdigits($_) == 1 || is_power(sumdigits($_))) } 1..1000; say "@seq"; # _Dana Jacobsen_, Oct 01 2015

%Y Cf. A001597, A007953.

%K easy,nonn,base

%O 1,2

%A _Zak Seidov_, Oct 10 2002

%E More terms from _Alois P. Heinz_, Sep 06 2015