A067071 -id:A067071 - cp's OEIS frontend

A066733 Numbers such that the product of the digits of its square is a square > 0.

1, 2, 3, 7, 12, 17, 21, 38, 88, 106, 107, 108, 109, 117, 122, 128, 129, 141, 146, 164, 168, 171, 173, 178, 191, 196, 204, 206, 207, 208, 209, 212, 221, 222, 236, 263, 276, 278, 288, 306, 342, 359, 364, 367, 372, 377, 394, 432, 463, 478, 479, 518, 537, 538

Offset: 1

Robert G. Wilson v, Jan 15 2002

			17 is in the sequence because the square of 17 is 289 and 2*8*9 = 144 = 12^2.

Harry J. Smith, Table of n, a(n) for n = 1..1000

Cf. A067071.

Do[a = Apply[Times, IntegerDigits[n^2]]; If[ a != 0 && IntegerQ[a^(1/2)], Print[n]], {n, 1, 10^4} ]
nzpQ[n_]:=Module[{prod=Times@@IntegerDigits[n^2]},prod!=0 && IntegerQ[ Sqrt[ prod]]]; Select[Range[600],nzpQ] (* Harvey P. Dale, May 27 2012 *)

isok(k)= { my(p=vecprod(digits(k^2))); p > 0 && issquare(p) } \\ Harry J. Smith, Mar 20 2010

A066734 Numbers such that the nonzero product of the digits of its 4th power is also a 4th power.

Original entry on oeis.org

1, 118, 144, 211, 427, 739, 1836, 8958, 19638, 20528, 21454, 22359, 24533, 26022, 27378, 29648, 33038, 33204, 33648, 40226, 40262, 46416, 47181, 47198, 49314, 53133, 55273, 55792, 59559, 59754, 60924, 61292, 61763, 61933, 66408, 68302

Offset: 1

Robert G. Wilson v, Jan 15 2002

			118 is in the sequence because the 4th power of 118 is 193877776 and 1*9*3*8*7*7*7*7*6 = 3111696 = 42^4.

Harry J. Smith, Table of n, a(n) for n = 1..1000

Cf. A067071.

Do[a = Apply[Times, IntegerDigits[n^2]]; If[ a != 0 && IntegerQ[a^(1/2)], Print[n]], {n, 1, 10^4} ]
d4pQ[n_]:=Module[{t=Times@@IntegerDigits[n^4]},t!=0&&IntegerQ[Surd[t,4]]]; Select[Range[70000],d4pQ] (* Harvey P. Dale, Feb 20 2018 *)

isok(k)={my(p=vecprod(digits(k^4))); p && ispower(p, 4)} \\ Harry J. Smith, Mar 20 2010

A067070 Cubes whose product of digits is a cube > 0.

Original entry on oeis.org

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

Amarnath Murthy, Jan 05 2002

			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.

Felice Russo, A set of new Smarandache Functions, Sequences and conjectures in number theory, American Research Press, Lupton USA.

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harry J. Smith)

Intersection of A237767 and A000578.

Cf. A007954, A052045, A052382, A067071.

pdcQ[n_]:=Module[{pd=Times@@IntegerDigits[n]},pd>0&&IntegerQ[ Surd[ pd,3]]]; Select[Range[3000]^3,pdcQ] (* Harvey P. Dale, Jun 01 2015 *)

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

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

a(n) = A067071(n)^3. - Andrew Howroyd, Dec 05 2024

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

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A066733 Numbers such that the product of the digits of its square is a square > 0.

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A066734 Numbers such that the nonzero product of the digits of its 4th power is also a 4th power.

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A067070 Cubes whose product of digits is a cube > 0.

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