cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A239219 Numbers n such that n^3 is not divisible by any of its nonzero digits.

Original entry on oeis.org

3, 7, 19, 29, 37, 43, 46, 59, 67, 77, 79, 86, 89, 127, 143, 149, 157, 163, 167, 169, 179, 187, 197, 199, 287, 299, 307, 313, 323, 337, 349, 353, 359, 367, 377, 379, 389, 397, 403, 419, 437, 443, 457, 460, 463, 587, 589, 593, 607, 613, 643, 647, 649, 653, 667
Offset: 1

Views

Author

Colin Barker, Mar 12 2014

Keywords

Examples

			37 is in the sequence because 37^3 = 50653 which is not divisible by 3, 5 or 6.

Links

Crossrefs

Cf. A239220, A239221, A239222.

Programs

  • Mathematica
    n3ndQ[n_]:=Module[{nzd=DeleteCases[IntegerDigits[n^3],0]},NoneTrue[ n^3/nzd,IntegerQ]]; Select[Range[700],n3ndQ] (* Harvey P. Dale, Aug 20 2022 *)
  • PARI
    isOK(n) = my(v=vecsort(digits(n^3), , 8)); for(i=1+(v[1]==0), #v, if(n^3%v[i]==0, return(0))); 1
s=[]; for(n=1, 1000, if(isOK(n), s=concat(s, n))); s

A239220 Cubes that are not divisible by any of their nonzero digits.

Original entry on oeis.org

27, 343, 6859, 24389, 50653, 79507, 97336, 205379, 300763, 456533, 493039, 636056, 704969, 2048383, 2924207, 3307949, 3869893, 4330747, 4657463, 4826809, 5735339, 6539203, 7645373, 7880599, 23639903, 26730899, 28934443, 30664297, 33698267, 38272753, 42508549
Offset: 1

Views

Author

Colin Barker, Mar 12 2014

Keywords

Comments

Intersection of A000578 and A038772.
Sequence is infinite because it contains (2*10^k + 3)^3, for k>1 and k not of the form 6*h + 2. - Giovanni Resta, Mar 13 2014

Examples

			50653 is in the sequence because 37^3 = 50653 is not divisible by 3, 5 or 6.

Links

Crossrefs

Cf. A239219, A239221, A239222.
Cf. A000578, A038772.

Programs

  • Mathematica
    ndnzdQ[n_]:=NoneTrue[n/Select[IntegerDigits[n],#!=0&],IntegerQ]; Select[ Range[ 400]^3,ndnzdQ] (* Harvey P. Dale, Jan 16 2022 *)
  • PARI
    isOK(n) = my(v=vecsort(digits(n^3), , 8)); for(i=1+(v[1]==0), #v, if(n^3%v[i]==0, return(0))); 1
s=[]; for(n=1, 1000, if(isOK(n), s=concat(s, n^3))); s

Formula

a(n) = A239219(n)^3. - Michel Marcus, Mar 19 2014

A239221 Numbers n such that n^3 is divisible by each of its nonzero digits.

Original entry on oeis.org

1, 2, 6, 10, 14, 20, 24, 42, 50, 60, 80, 100, 102, 126, 132, 140, 168, 180, 200, 202, 204, 210, 222, 234, 240, 246, 252, 270, 324, 342, 348, 350, 354, 360, 390, 396, 402, 420, 440, 450, 456, 462, 474, 480, 500, 504, 510, 522, 546, 552, 570, 588, 600, 612
Offset: 1

Views

Author

Colin Barker, Mar 12 2014

Keywords

Examples

			42 is in the sequence because 42^3 = 74088 which is divisible by 4, 7 and 8.

Links

Crossrefs

Cf. A239219, A239220, A239222.

Programs

  • Mathematica
    Select[Range[700],Union[PowerMod[#,3,IntegerDigits[#^3]/.(0-> Nothing)]] == {0}&] (* Harvey P. Dale, Jan 17 2021 *)
  • PARI
    isOK(n) = my(v=vecsort(digits(n^3), , 8)); for(i=1+(v[1]==0), #v, if(n^3%v[i], return(0))); 1
s=[]; for(n=1, 1000, if(isOK(n), s=concat(s, n))); s
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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