A117224 Numbers for which the square and the cube have the same digital sum.

0, 1, 3, 6, 10, 24, 28, 30, 37, 60, 64, 81, 87, 93, 100, 114, 118, 136, 163, 219, 222, 228, 234, 240, 252, 258, 267, 273, 276, 280, 291, 294, 300, 312, 316, 342, 343, 370, 384, 387, 433, 447, 468, 469, 477, 478, 507, 525, 534, 537, 541, 585, 591, 600, 606, 613

Offset: 1

Author

Luc Stevens (lms022(AT)yahoo.com), Apr 21 2006

Keywords

• nonn
• easy
• base

Examples

			24 is in the sequence because 24^2 = 576, 24^3 = 13824 and 5 + 7 + 6 = 1 + 3 + 8 + 2 + 4.
		

Links

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

Crossrefs

Cf. A058369.

Programs

Magma

[n: n in [0..613] | &+Intseq(n^2) eq &+Intseq(n^3)];  // Bruno Berselli, Jun 28 2011

Maple

a:=proc(n) local nn,nnn: nn:=convert(n^2,base,10): nnn:=convert(n^3,base,10): if sum(nn[i],i=1..nops(nn))=sum(nnn[j],j=1..nops(nnn)) then n else fi end: seq(a(n),n=0..620); # Emeric Deutsch, Apr 27 2006

Mathematica

scdsQ[n_]:=Total[IntegerDigits[n^2]]==Total[IntegerDigits[n^3]]; Select[ Range[ 0,700],scdsQ] (* Harvey P. Dale, Jan 23 2019 *)

PARI

is(n) = sumdigits(n^2) == sumdigits(n^3) \\ David A. Corneth, Sep 05 2020

Extensions

Offset corrected by Arkadiusz Wesolowski, Jun 28 2011