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.

A015859 Numbers k such that phi(k) | sigma(k + 12).

Original entry on oeis.org

1, 2, 3, 10, 12, 14, 15, 16, 18, 21, 26, 30, 35, 39, 42, 44, 54, 65, 75, 76, 90, 108, 123, 126, 153, 156, 165, 218, 234, 252, 270, 364, 366, 370, 396, 462, 474, 494, 508, 525, 540, 558, 615, 620, 630, 646, 702, 732, 814, 852, 858, 918, 980, 1022, 1044
Offset: 1

Views

Author

Robert G. Wilson v

Keywords

Links

Crossrefs

Cf. A015834 (m=1), A015837 (m=2), A015840 (m=3), A015841 (m=4), A015843 (m=5), A015844 (m=6), A015845 (m=7), A015851 (m=8), A015853 (m=9), A015856 (m=10), A015858 (m=11), this sequence (m=12), A015860 (m=13).

Programs

  • Magma
    [n: n in [1..900] | DivisorSigma(1,n+12) mod EulerPhi(n) eq 0]; // G. C. Greubel, Dec 13 2018
  • Mathematica
    Select[Range[1100],Divisible[DivisorSigma[1,#+12],EulerPhi[#]]&] (* Harvey P. Dale, Jun 01 2018 *)
  • PARI
    is(n)=!(sigma(n+12)%eulerphi(n)) \\ Charles R Greathouse IV, Sep 25 2012

Extensions

Missing a(1)=1 inserted by Sean A. Irvine, Dec 13 2018

A015860 Numbers k such that phi(k) | sigma(k + 13).

Original entry on oeis.org

1, 2, 4, 6, 7, 8, 9, 10, 11, 15, 20, 25, 27, 34, 38, 41, 42, 44, 56, 57, 64, 66, 80, 82, 120, 122, 128, 146, 152, 155, 164, 176, 204, 222, 237, 310, 330, 331, 342, 377, 378, 400, 427, 460, 465, 490, 500, 504, 560, 602, 610, 626, 704, 722, 770, 817, 861
Offset: 1

Views

Author

Robert G. Wilson v

Keywords

Links

Crossrefs

Cf. A015834 (m=1), A015837 (m=2), A015840 (m=3), A015841 (m=4), A015843 (m=5), A015844 (m=6), A015845 (m=7), A015851 (m=8), A015853 (m=9), A015856 (m=10), A015858 (m=11), A015859 (m=12), this sequence (m=13).

Programs

  • Magma
    [n: n in [1..900] | DivisorSigma(1,n+13) mod EulerPhi(n) eq 0]; // G. C. Greubel, Dec 13 2018
  • Mathematica
    Select[Range[900], Mod[DivisorSigma[1, #+13], EulerPhi[#]]==0 &] (* G. C. Greubel, Dec 13 2018 *)
  • PARI
    is(n)=!(sigma(n+13)%eulerphi(n)) \\ Charles R Greathouse IV, Sep 25 2012

Extensions

Missing a(1)=1 inserted by Sean A. Irvine, Dec 13 2018

A015853 Numbers k such that phi(k) | sigma(k + 9).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 10, 12, 13, 14, 21, 24, 26, 30, 31, 37, 42, 45, 48, 50, 57, 60, 68, 76, 78, 96, 105, 111, 133, 156, 168, 175, 181, 196, 200, 215, 273, 286, 288, 290, 310, 320, 336, 350, 361, 369, 381, 399, 406, 420, 450, 465, 543, 585, 600, 612, 656, 740
Offset: 1

Views

Author

Robert G. Wilson v

Keywords

Links

Crossrefs

Cf. A015834 (m=1), A015837 (m=2), A015840 (m=3), A015841 (m=4), A015843 (m=5), A015844 (m=6), A015845 (m=7), A015851 (m=8), this sequence (m=9), A015856 (m=10), A015858 (m=11), A015859 (m=12), A015860 (m=13).

Programs

  • Magma
    [n: n in [1..900] | DivisorSigma(1,n+9) mod EulerPhi(n) eq 0]; // G. C. Greubel, Dec 13 2018
  • Mathematica
    Select[Range[1000], Divisible[DivisorSigma[1,#+9], EulerPhi[#]] &] (* Amiram Eldar, Dec 13 2018 *)
  • PARI
    is(n)=!(sigma(n+9)%eulerphi(n)) \\ Charles R Greathouse IV, Sep 25 2012

Extensions

Missing a(1)=1 inserted by Sean A. Irvine, Dec 13 2018

A015856 Numbers k such that phi(k) | sigma(k + 10).

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 12, 13, 14, 20, 28, 29, 32, 36, 44, 45, 52, 53, 56, 60, 66, 77, 84, 86, 104, 105, 108, 110, 123, 130, 144, 172, 221, 228, 238, 270, 287, 312, 342, 366, 380, 385, 396, 441, 468, 558, 584, 585, 588, 644, 672, 750, 754, 760, 854, 864
Offset: 1

Views

Author

Robert G. Wilson v

Keywords

Links

Crossrefs

Cf. A015834 (m=1), A015837 (m=2), A015840 (m=3), A015841 (m=4), A015843 (m=5), A015844 (m=6), A015845 (m=7), A015851 (m=8), A015853 (m=9), this sequence (m=10), A015858 (m=11), A015859 (m=12), A015860 (m=13).

Programs

  • Magma
    [n: n in [1..900] | DivisorSigma(1,n+10) mod EulerPhi(n) eq 0]; // G. C. Greubel, Dec 13 2018
  • Mathematica
    Select[Range[1000], Divisible[DivisorSigma[1,#+10], EulerPhi[#]] &] (* Amiram Eldar, Dec 13 2018 *)
  • PARI
    is(n)=!(sigma(n+10)%eulerphi(n)) \\ Charles R Greathouse IV, Sep 25 2012

Extensions

Missing a(1)=1 inserted by Sean A. Irvine, Dec 13 2018

A172333 Numbers m such that m and m+22 have the same sum of divisors.

Original entry on oeis.org

57, 85, 213, 224, 354, 476, 568, 594, 812, 1218, 1235, 1316, 1484, 2103, 2470, 2492, 2643, 2840, 2996, 3836, 3978, 4026, 4544, 4810, 4844, 5012, 6125, 6356, 6524, 7364, 7532, 7648, 8876, 9272, 9328, 10098, 11107, 11797, 12572, 12594, 13412, 13640
Offset: 1

Views

Author

Michel Lagneau, Feb 01 2010

Keywords

Comments

If 3*k-1 and 14*k-1 are both prime with k>1, then n = 28*(3*k-1) belongs to this sequence. The number of such integers n <= x would be asymptotically cx/(log x)^2 for some constant c > 0 from the Hardy-Littlewood conjecture D in Partitio Numerorum. - Tomohiro Yamada, Oct 03 2018

References

  • J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 62, p. 22, Ellipses, Paris 2008.
  • W. Sierpinski, A Selection of Problems in the Theory of Numbers. Macmillan, NY, 1964, p. 110.
  • Tomohiro Yamada, On equations sigma(n) = sigma(n+k) and phi(n) = phi(n+k), J. Comb. Number Theory 9 (2017), 15-21.

Links

Crossrefs

Cf. A000203, A015861, A002961, A015865, A015867, A015858, A015859, A015860.

Programs

  • GAP
    Filtered([1..13700],k->Sigma(k)=Sigma(k+22)); # Muniru A Asiru, Oct 20 2018
  • Maple
    with(numtheory):for n from 1 to 20000 do;if sigma(n) = sigma(n+22) then print(n); else fi ; od;
  • PARI
    isok(k) = sigma(k)==sigma(k+22); \\ Altug Alkan, Oct 03 2018
Showing 1-5 of 5 results.

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

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