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 1-6 of 6 results.

A136540 Numbers n such that sigma(n) = 7*phi(n).

Original entry on oeis.org

12, 78, 140, 910, 2214, 4180, 4674, 8008, 16120, 25758, 27170, 46816, 54530, 58302, 94240, 99484, 116116, 200260, 233740, 257140, 264160, 350740, 371898, 383656, 479864, 518022, 523218, 551540, 561340, 575598, 616722, 646646, 785118, 965960, 1027000
Offset: 1

Views

Author

Farideh Firoozbakht, Jan 05 2008

Keywords

Comments

If 2^p-1 is a Mersenne prime greater than 3 then m = 65*2^(p-2)*(2^p-1) is in the sequence (the proof is easy).

Examples

			sigma(12) = 28 = 7*phi(12) so 12 is in the sequence.

Links

Crossrefs

Cf. A000043, A000668, A068390, A104900, A104901, A104902, A104903.

Programs

  • Maple
    with(numtheory): A136540:=n->`if`(sigma(n)=7*phi(n), n, NULL): seq(A136540(n), n=1..10^5); # Wesley Ivan Hurt, Feb 11 2017
  • Mathematica
    Do[If[DivisorSigma[1,n]==7*EulerPhi[n],Print[n]],{n,600000}]
(* Second program *)
Select[Range[10^6], DivisorSigma[1, #] == 7 EulerPhi@ # &] (* Michael De Vlieger, Feb 12 2017 *)
  • PARI
    is(n)=sigma(n)==7*eulerphi(n) \\ Charles R Greathouse IV, May 09 2013

A171256 Numbers n such that sigma(n) = 10*phi(n) (where sigma=A000203, phi=A000010).

Original entry on oeis.org

168, 270, 570, 2376, 2436, 5016, 6426, 7110, 13566, 15834, 34452, 58520, 62568, 72732, 75210, 113832, 126882, 168756, 169218, 191862, 199368, 223938, 240312, 280488, 308568, 321468, 420888, 449442, 472758, 661848, 673608, 776736, 848540, 854496, 907236
Offset: 1

Views

Author

M. F. Hasler, Mar 19 2010

Keywords

Comments

If n is in this sequence, then for any prime p not dividing n, sigma(np) - 10*phi(np) = 2*sigma(n).

Links

Crossrefs

Cf. A062699, A068391, A074400, A068390, A136547, A104900, A136540, A104901, A163667, A171257, A104902, A171258, A171259, A171260, A104903.

Programs

  • Mathematica
    Select[Range[10^6], DivisorSigma[1, #] == 10 * EulerPhi[#] &] (* Amiram Eldar, Dec 04 2019 *)
  • PARI
    for(k=1,10^6, sigma(k) - 10*eulerphi(k) || print1(k", "));

A171257 Numbers n such that sigma(n) = 11*phi(n) (where sigma=A000203, phi=A000010).

Original entry on oeis.org

2580, 16770, 18630, 28896, 35970, 61404, 66024, 147576, 163944, 215124, 224010, 296184, 399126, 408672, 443394, 464340, 476010, 574308, 856086, 862752, 868428, 931224, 957348, 1004910, 1110186, 1496610, 1721720, 1723290, 1833348, 1971288, 2139852, 2234790
Offset: 1

Views

Author

Farideh Firoozbakht and M. F. Hasler, Mar 19 2010

Keywords

Links

Crossrefs

Cf. A062699, A068391, A068390, A136547, A104900, A136540, A104901, A163667, A171256, A104902, A171258, A171259, A171260, A104903.

Programs

  • Mathematica
    Select[Range[10^6], DivisorSigma[1, #] == 11 * EulerPhi[#] &] (* Amiram Eldar, Dec 04 2019 *)
  • PARI
    for(k=1,2e6, sigma(k) - 11*eulerphi(k) || print1(k", "));

A171258 Numbers n such that sigma(n) = 13*phi(n) (where sigma=A000203, phi=A000010).

Original entry on oeis.org

630, 5544, 11160, 18810, 27000, 57000, 80388, 161820, 178020, 182880, 242820, 265608, 388620, 391500, 447678, 465192, 522522, 671760, 690120, 711000, 775170, 826500, 901170, 1051830, 1102290, 1157130, 1418160, 1578330, 1679400, 1812384, 1874520, 1993824
Offset: 1

Views

Author

Farideh Firoozbakht and M. F. Hasler, Mar 19 2010

Keywords

Links

Crossrefs

Cf. A062699, A068391, A068390, A136547, A104900, A136540, A104901, A163667, A171256, A171257, A104902, A171259, A171260, A104903.

Programs

  • Mathematica
    Select[Range[2*10^6],DivisorSigma[1,#]==13EulerPhi[#]&] (* Harvey P. Dale, Mar 29 2018 *)
  • PARI
    for(k=1,2e6, sigma(k) - 13*eulerphi(k) || print1(k", "));

A171259 Numbers n such that sigma(n) = 14*phi(n) (where sigma=A000203, phi=A000010).

Original entry on oeis.org

420, 2730, 5940, 12540, 24024, 38610, 48360, 66528, 77490, 81510, 133920, 140448, 141372, 156420, 163590, 282720, 284580, 298452, 348348, 498420, 600780, 681912, 701220, 771420, 792480, 901530, 918918, 1016730, 1052220, 1150968, 1372680, 1439592, 1654620
Offset: 1

Views

Author

Farideh Firoozbakht and M. F. Hasler, Mar 19 2010

Keywords

Links

Crossrefs

Cf. A062699, A068391, A068390, A136547, A104900, A136540, A104901, A163667, A171256, A171257, A104902, A171258, A171260, A104903.

Programs

  • Mathematica
    Select[Range[10^6], DivisorSigma[1, #] == 14 * EulerPhi[#] &] (* Amiram Eldar, Dec 04 2019 *)
  • PARI
    for(k=1,2e6, sigma(k) - 14*eulerphi(k) || print1(k", "));

A171260 Numbers n such that sigma(n) = 15*phi(n) (where sigma=A000203, phi=A000010).

Original entry on oeis.org

840, 11880, 12180, 25080, 32130, 67830, 79170, 172260, 282744, 312840, 363660, 569160, 596904, 634410, 696696, 843780, 846090, 959310, 996840, 1119690, 1201560, 1402440, 1542840, 1607340, 1929312, 2104440, 2247210, 2363790, 3309240, 3368040, 3883680
Offset: 1

Views

Author

Farideh Firoozbakht and M. F. Hasler, Mar 19 2010

Keywords

Links

Crossrefs

Cf. A062699, A068391, A068390, A136547, A104900, A136540, A104901, A163667, A171256, A171257, A104902, A171258, A171259, A104903.

Programs

  • Mathematica
    Select[Range[10^6], DivisorSigma[1, #] == 15 * EulerPhi[#] &] (* Amiram Eldar, Dec 04 2019 *)
  • PARI
    for(k=1,3e6, sigma(k) - 15*eulerphi(k) || print1(k", "));
Showing 1-6 of 6 results.

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