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.

A115905 Numbers k such that k + phi(k) is a triangular number.

Original entry on oeis.org

2, 4, 9, 11, 20, 23, 25, 27, 49, 53, 92, 93, 105, 121, 127, 147, 150, 163, 169, 220, 228, 231, 233, 281, 286, 289, 294, 332, 361, 431, 474, 529, 541, 543, 548, 613, 660, 675, 710, 726, 743, 825, 827, 841, 888, 891, 961, 977, 993, 1014, 1028, 1265, 1310, 1369
Offset: 1

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Examples

			121 + phi(121) = 231 = T(21).

Links

Crossrefs

Cf. A000010, A000217, A069066, A115908, A115910.

Programs

  • Mathematica
    Select[Range[1500],OddQ[Sqrt[8(#+EulerPhi[#])+1]]&] (* Harvey P. Dale, May 11 2015 *)
  • PARI
    isok(n) = ispolygonal(n + eulerphi(n), 3); \\ Michel Marcus, Jan 25 2014

A115904 Numbers k such that k + sigma(k) is a triangular number.

Original entry on oeis.org

7, 10, 66, 136, 145, 196, 198, 234, 270, 438, 495, 528, 592, 606, 855, 910, 1045, 1158, 1428, 2208, 2718, 2922, 3016, 3663, 3808, 3916, 4506, 4975, 5043, 5136, 5598, 6366, 6600, 7080, 7498, 7821, 8172, 8200, 8217, 8814, 9318, 9730, 9738
Offset: 1

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Examples

			234 + sigma(234) = 780 = T(39).

Links

Crossrefs

Cf. A069066, A115907, A115909.

Programs

  • Mathematica
    trnoQ[n_]:=IntegerQ[(Sqrt[1+8n]-1)/2]; Select[Range[10000], trnoQ[#+ DivisorSigma[ 1,#]]&] (* Harvey P. Dale, Apr 26 2014 *)
  • PARI
    isok(n) = ispolygonal(n + sigma(n), 3); \\ Michel Marcus, Jan 25 2014

A115906 Numbers k such that k + sigma(k) + phi(k) is a triangular number.

Original entry on oeis.org

1, 2, 5, 7, 9, 16, 144, 186, 410, 656, 680, 805, 963, 968, 1152, 1331, 1419, 1476, 1557, 1608, 2158, 2220, 2376, 2401, 2529, 2840, 3376, 3447, 3570, 3591, 4018, 5030, 5769, 5967, 6530, 6720, 6854, 6955, 7250, 7856, 8004, 8514, 8946, 9144
Offset: 1

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Examples

			1331 + sigma(1331) + phi(1331) = 4005 = T(89).

Links

Crossrefs

Cf. A000010, A000203, A000217, A069066, A115904, A115905.

Programs

  • PARI
    isok(n) = {my(f=factor(n)); ispolygonal(n + sigma(f) + eulerphi(f), 3);} \\ Amiram Eldar, Apr 06 2023

A115911 Numbers k such that phi(k)*sigma(k) is a triangular number.

Original entry on oeis.org

1, 2, 9, 11, 23, 118, 373, 556, 1332, 2420, 3081, 5251, 7642, 12671, 116836, 127627, 135861, 172676, 198912, 365408, 421902, 426710, 901273, 921736, 954068, 1001396, 1003333, 1006567, 1077452, 1161754, 1162514, 1364225, 1632361
Offset: 1

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Examples

			phi(1003333)*sigma(1003333) = 1003888529280 = T(1416960).

Links

Crossrefs

Cf. A062354, A069066.

Programs

  • Mathematica
    Select[Range[10^4], IntegerQ @ Sqrt[8 * EulerPhi[#] * DivisorSigma[1, #] + 1] &] (* Amiram Eldar, Sep 16 2019 *)
  • PARI
    isok(n) = ispolygonal(eulerphi(n)*sigma(n), 3); \\ Michel Marcus, Jan 09 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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