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

A239222 Cubes that are divisible by each of their nonzero digits.

Original entry on oeis.org

1, 8, 216, 1000, 2744, 8000, 13824, 74088, 125000, 216000, 512000, 1000000, 1061208, 2000376, 2299968, 2744000, 4741632, 5832000, 8000000, 8242408, 8489664, 9261000, 10941048, 12812904, 13824000, 14886936, 16003008, 19683000, 34012224, 40001688, 42144192
Offset: 1

Views

Author

Colin Barker, Mar 12 2014

Keywords

Comments

Intersection of A000578 and A002796.

Examples

			74088 is in the sequence because 74088 is divisible by 4, 7 and 8.

Links

Crossrefs

Cf. A239219, A239220, A239221.
Cf. A000578, A002796.

Programs

  • Mathematica
    dedQ[n_]:=And@@Divisible[n,Select[IntegerDigits[n],#>0&]]; Select[ Range[ 400]^3, dedQ] (* Harvey P. Dale, Apr 25 2015 *)
  • 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^3))); s

Formula

a(n) = A239221^(n)^3. - Michel Marcus, Mar 19 2014
Showing 1-3 of 3 results.

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

Content is available under The OEIS End-User License Agreement.