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A067070
Cubes whose product of digits is a cube > 0.
1
1, 8, 24389, 226981, 9393931, 11239424, 17373979, 36264691, 66923416, 94818816, 348913664, 435519512, 463684824, 549353259, 555412248, 743677416, 3929352552, 4982686912, 5526456832, 11329982936, 12374478297, 12681938368, 15142552424
OFFSET
1,2
REFERENCES
Felice Russo, A set of new Smarandache Functions, Sequences and conjectures in number theory, American Research Press, Lupton USA.
LINKS
David A. Corneth, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harry J. Smith)
FORMULA
a(n) = A067071(n)^3. - Andrew Howroyd, Dec 05 2024
EXAMPLE
24389 is in the sequence because (1) it is a cube and (2) the product of its digits is 2*4*3*8*9, = 1728 which is a cube > 0.
MATHEMATICA
pdcQ[n_]:=Module[{pd=Times@@IntegerDigits[n]}, pd>0&&IntegerQ[ Surd[ pd, 3]]]; Select[Range[3000]^3, pdcQ] (* Harvey P. Dale, Jun 01 2015 *)
PROG
(PARI) isA237767(k)={my(p=vecprod(digits(k))); p && ispower(p, 3)}
{ for (m=1, 2500, if(isA237767(m^3), print1(m^3, ", "))) } \\ Harry J. Smith, May 04 2010
(PARI)
first(n) = {
my(res = List(), c, vp, i);
for(i = 1, oo,
c = i^3;
vp = vecprod(digits(c));
if(vp && ispower(vp, 3),
listput(res, c);
if(#res >= n,
return(Vec(res))
)
)
)
} \\ David A. Corneth, Dec 01 2023
CROSSREFS
Intersection of A237767 and A000578.
Sequence in context: A067074 A220942 A281359 * A115478 A221629 A362280
KEYWORD
nonn,base
AUTHOR
Amarnath Murthy, Jan 05 2002
EXTENSIONS
More terms from Sascha Kurz, Mar 23 2002
One further term from Luc Stevens (lms022(AT)yahoo.com), May 03 2006
Edited by R. J. Mathar, Aug 08 2008
Offset changed from 0 to 1 by Harry J. Smith, May 04 2010
STATUS
approved