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A075783 Additive perfect powers: sum-of-digits is also a perfect power. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 18 10:05 EDT 2019. Contains 328146 sequences. (Running on oeis4.)