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 1-5 of 5 results.

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 *)

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 *)

A116016 n+prime(n)+prime(prime(n)) is a cube, where prime(n) is the n-th prime.

Original entry on oeis.org

34780, 147895, 302689, 449410, 4801151, 6717665
Offset: 1

Views

Author

Giovanni Resta, Feb 13 2006

Keywords

Examples

			34780+prime(34780)+prime(prime(34780)) = 6434856 = 186^3.

Crossrefs

Cf. A116011, A116012.

Programs

  • PARI
    isok(n) = ispower(n + prime(n) + prime(prime(n)), 3); \\ Michel Marcus, Jan 27 2014

A116023 The n-th prime plus n gives a semiprime (A001358).

Original entry on oeis.org

10, 12, 14, 15, 16, 19, 20, 21, 23, 25, 30, 31, 36, 37, 38, 39, 40, 44, 52, 54, 56, 57, 58, 60, 62, 67, 74, 75, 77, 80, 83, 84, 86, 88, 90, 99, 107, 111, 115, 120, 124, 136, 140, 145, 146, 154, 156, 160, 162, 164, 165, 166, 168, 174, 175, 182, 189, 192, 195, 196
Offset: 1

Views

Author

Giovanni Resta, Feb 13 2006

Keywords

Examples

			p(30)+30=143=11*13.

Crossrefs

Cf. A001358, A116012, A116024, A014688
Showing 1-5 of 5 results.

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

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