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

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 *)

A116015 n+sigma(n)+sigma(sigma(n)) is a triangular number.

Original entry on oeis.org

1, 9, 43, 109, 119, 161, 175, 192, 232, 490, 843, 1050, 1162, 1242, 1635, 1959, 2113, 2859, 2935, 3008, 3174, 3469, 3717, 4165, 4173, 4761, 4839, 4876, 5200, 6111, 6423, 6468, 8008, 8480, 9064, 9523, 9603, 11143, 11197, 11353, 11557, 11773
Offset: 1

Views

Author

Giovanni Resta, Feb 13 2006

Keywords

Examples

			6111+sigma(6111)+sigma(sigma(6111))=T(286).

Crossrefs

Cf. A116012, A116013, A116014.

Programs

  • Mathematica
    triangularQ[n_] := IntegerQ[Sqrt[8n + 1]]; Reap[For[n = 1, n < 12000, n++, s = DivisorSigma[1, n]; If[triangularQ[n + s + DivisorSigma[1, s]], Sow[n]]]][[2, 1]] (* Jean-François Alcover, Oct 15 2013 *)

A116025 sigma(n) plus n gives a semiprime (A001358).

Original entry on oeis.org

7, 9, 14, 15, 17, 18, 19, 20, 22, 32, 39, 43, 45, 46, 47, 49, 50, 51, 59, 61, 62, 68, 70, 71, 72, 79, 81, 86, 91, 93, 95, 101, 104, 107, 109, 110, 115, 116, 117, 118, 121, 123, 129, 130, 142, 149, 151, 158, 160, 163, 164, 165, 167, 177, 185, 187, 197, 201, 207
Offset: 1

Views

Author

Giovanni Resta, Feb 13 2006

Keywords

Examples

			sigma(101)+101=203=7*29.

Links

Crossrefs

Cf. A001358, A116014.

Programs

  • Mathematica
    Select[Range[300],PrimeOmega[DivisorSigma[1,#]+#]==2&] (* Harvey P. Dale, May 21 2014 *)
Showing 1-4 of 4 results.

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

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