A075783 Additive perfect powers: sum-of-digits is also a perfect power.

1, 4, 8, 9, 27, 36, 81, 100, 121, 125, 144, 169, 196, 216, 225, 243, 324, 400, 441, 484, 512, 529, 900, 961, 1000, 1331, 1521, 1681, 2025, 2304, 2601, 3364, 3481, 3600, 3969, 4489, 4624, 5776, 5929, 7225, 7396, 7569, 7776, 8000, 8100, 8649, 8836, 9025, 10000

Offset

1,2

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Example

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

Mathematica

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 *)

Prog

(PARI) isok(n) = (n==1 || ispower(n)) && (sumdigits(n)==1 || ispower(sumdigits(n))) \\ Dana Jacobsen, Oct 01 2015
(Perl) use ntheory ":all"; my @seq = grep { ($_==1 || is_power($_)) && (sumdigits($_) == 1 || is_power(sumdigits($_))) } 1..1000; say "@seq"; # Dana Jacobsen, Oct 01 2015

Crossrefs

Cf. A001597, A007953.

Sequence in context: A171468 A114377 A115697 * A098121 A115656 A076705

Adjacent sequences: A075780 A075781 A075782 * A075784 A075785 A075786

Keyword

easy,nonn,base

Author

Zak Seidov, Oct 10 2002

Extensions

More terms from Alois P. Heinz, Sep 06 2015

Status

approved