

A118719


Cubes for which the digital root is also a cube.


5



0, 1, 8, 64, 125, 343, 512, 1000, 1331, 2197, 2744, 4096, 4913, 6859, 8000, 10648, 12167, 15625, 17576, 21952, 24389, 29791, 32768, 39304, 42875, 50653, 54872, 64000, 68921, 79507, 85184, 97336, 103823, 117649, 125000, 140608, 148877
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OFFSET

1,3


COMMENTS

All cubes have a digital root 1,8 or 9. (except for the number 0) So this sequence contains all cubes with a digital root which is not 9.
This sequence is 0 union A016779 union A016791.


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..3000


FORMULA

a(n) = (floor(3*n/2)2)^3 for n >= 2.  Nathaniel Johnston, May 05 2011
G.f.: x^2*(1+7*x+53*x^2+40*x^3+53*x^4+7*x^5+x^6)/((1+x)^3*(1x)^4). a(n) = A001651(n1)^3 for n>1.  Bruno Berselli, May 05 2011


EXAMPLE

64 is in the sequence because (1) it is a cube and (2) the digital root 1 is also a cube.


PROG

(MAGMA) [0] cat [(6*n+(1)^n9)^3 div 64: n in [2..37]]; // Bruno Berselli, May 05 2011
(PARI) a010888(n)=if(n, (n1)%9+1)
lista(nn) = {for (n=0, nn, if (ispower(a010888(n^3), 3), print1(n^3, ", ")); ); } \\ Michel Marcus, Feb 18 2015


CROSSREFS

Cf. A000578, A010888, A116978.
Sequence in context: A208380 A160428 A074102 * A134739 A116978 A125110
Adjacent sequences: A118716 A118717 A118718 * A118720 A118721 A118722


KEYWORD

base,easy,nonn


AUTHOR

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


STATUS

approved



