A067070 Cubes for which the product of the digits is a cube > 0.

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)

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) ProdD(x)= { local(p=1); while (x>9 && p>0, p*=x%10; x\=10); return(p*x) }
iscube(x)= { if (x==0, return(1)); f=factor(x)~; for(i=1, length(f), if (t=f[2, i]%3, return(0))); return(1); }
{ n=0; for (m=1, 10^10, p=ProdD(m^3); if (p && iscube(p), n++; print1(m^3, ", "); if (n==100, return)) ) } \\ Harry J. Smith, May 04 2010
(PARI)
first(n) = {
	my(res = List(), c, f, vp, i);
	for(i = 1, oo,
		c = i^3;
		vp = vecprod(digits(c));
		if(vp == 0,
			next
		);
		f = factor(vp);
		if(gcd(f[, 2])%3 == 0,
			listput(res, c);
			if(#res >= n,
				return(res)
			)
		)
	)
} \\ David A. Corneth, Dec 01 2023

Crossrefs

Cf. A000578, A007954, A052045, A052382.

Sequence in context: A067074 A220942 A281359 * A115478 A221629 A362280

Adjacent sequences: A067067 A067068 A067069 * A067071 A067072 A067073

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