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

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 *)

A116024 The n-th prime minus n gives a semiprime (A001358).

Original entry on oeis.org

5, 7, 9, 12, 20, 22, 24, 36, 40, 49, 52, 55, 58, 59, 60, 64, 69, 72, 74, 78, 80, 82, 87, 93, 96, 101, 105, 106, 108, 112, 114, 117, 118, 122, 123, 124, 125, 128, 132, 134, 135, 136, 138, 140, 142, 147, 150, 156, 158, 159, 160, 162, 164, 166, 170, 172, 180, 184
Offset: 1

Views

Author

Giovanni Resta, Feb 13 2006

Keywords

Examples

			p(40)-40=133=7*19.

Links

Crossrefs

Cf. A001358, A116013, A116023.

Programs

  • Mathematica
    Transpose[Select[Table[{Prime[n],n},{n,200}],PrimeOmega[#[[1]]-#[[2]]] == 2&]][[2]] (* Harvey P. Dale, Jun 05 2015 *)
Showing 1-4 of 4 results.

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

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