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 1-4 of 4 results.

A116012 Numbers k such that k + sigma(k) + sigma(sigma(k)) is a fourth power.

Original entry on oeis.org

19, 1873, 147497, 792736, 4551733, 4967176, 7333813, 8539521, 8674128, 12388853, 12948373, 18331664, 24834369, 36294936, 50952310, 116340016, 170434387, 196966352, 222505713, 236504256, 286766145, 390771936, 426323088, 532998481, 778930925, 805653001
Offset: 1

Views

Author

Giovanni Resta, Feb 13 2006

Keywords

Examples

			792736 + sigma(792736) + sigma(sigma(792736)) = 56^4.

Crossrefs

Cf. A116013, A116014, A116015.

Programs

  • PARI
    for(n=1, 10^9, s=sigma(n); if(ispower(n+s+sigma(s), 4), print(n))) /* Donovan Johnson, Feb 17 2013 */

Extensions

a(5)-a(26) from Donovan Johnson, Feb 17 2013

A116014 Numbers k such that k + sigma(k) + sigma(sigma(k)) is a square.

Original entry on oeis.org

2, 9, 19, 98, 141, 176, 319, 396, 467, 691, 729, 970, 1113, 1279, 1447, 1473, 1873, 1974, 2403, 3712, 5208, 5965, 6777, 7183, 8353, 8769, 8881, 8962, 10137, 10180, 10771, 11314, 12016, 12241, 13624, 15196, 19683, 19705, 20053, 20553, 21241
Offset: 1

Views

Author

Giovanni Resta, Feb 13 2006

Keywords

Examples

			1113 + sigma(1113) + sigma(sigma(1113)) = 89^2.

Links

Crossrefs

Cf. A116012, A116013, A116015.

Programs

  • Mathematica
    okQ[n_]:=Module[{dsn=DivisorSigma[1,n]}, IntegerQ[Sqrt[n+dsn+DivisorSigma[1,dsn]]]]; Select[Range[22000],okQ]  (* Harvey P. Dale, Jan 23 2011 *)
  • PARI
    is(n)=my(s=sigma(n)); issquare(n+s+sigma(s)) \\ Charles R Greathouse IV, Jul 30 2016

A116013 n+sigma(n)+sigma(sigma(n)) is a cube.

Original entry on oeis.org

517, 1403, 2467, 28265, 28580, 49888, 52396, 77429, 81099, 290936, 319600, 394731, 462803, 555543, 601943, 617716, 633065, 634808, 720401, 775669, 884835, 894024, 1077432, 1089360, 1170136, 1178152, 1191789, 1209357
Offset: 1

Views

Author

Giovanni Resta, Feb 13 2006

Keywords

Examples

			1403+sigma(1403)+sigma(sigma(1403))=19^3.

Crossrefs

Cf. A116012, A116014, A116015.

Programs

  • Mathematica
    scQ[n_]:=Module[{c=DivisorSigma[1,n]},IntegerQ[(n+c+DivisorSigma[1,c]) ^ (1/3)]]; Select[Range[1300000],scQ] (* Harvey P. Dale, Dec 17 2012 *)

A116026 phi(n) plus n gives a semiprime (A001358).

Original entry on oeis.org

4, 5, 9, 10, 11, 13, 17, 21, 26, 29, 30, 43, 45, 47, 49, 55, 57, 58, 61, 66, 67, 70, 71, 73, 75, 82, 87, 89, 99, 101, 102, 103, 106, 107, 109, 111, 115, 119, 123, 127, 129, 130, 146, 151, 153, 154, 175, 181, 182, 183, 185, 190, 191, 195, 197, 202, 203, 205, 207
Offset: 1

Views

Author

Giovanni Resta, Feb 13 2006

Keywords

Examples

			phi(101)+101=201=3*67.

Crossrefs

Cf. A001358, A116015.
Showing 1-4 of 4 results.

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

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