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 1-9 of 9 results.

A274566 Numbers k such that sigma(k) == 0 (mod k-10).

Original entry on oeis.org

6, 9, 11, 12, 14, 22, 40, 42, 46, 154, 190, 2656, 6490, 44650, 318250, 1360810, 1503370, 1788490, 3214090, 103712410, 3915380170, 6077111050, 9796360330, 10828121356, 33086522327050, 35966517350410, 11577093570201610, 16726040141635450, 576460762503970816
Offset: 1

Views

Author

Paolo P. Lava, Jul 06 2016

Keywords

Examples

			sigma(11) mod (11 - 10) = 12 mod 1 = 0.

Crossrefs

Contains subsequence A223607.
Contains 2 * odd terms of A101223.
Cf. A045770, A067702, A088833, A181598, A274551, A274552, A274553, A274554, A274556, A274557, A274558, A274559, A274560, A274561, A274562, A274563, A274564, A274565.

Programs

  • Magma
    [n: n in [1..2*10^6] | n ne 10 and SumOfDivisors(n) mod (n-10) eq 0 ]; // Vincenzo Librandi, Jul 06 2016
  • Mathematica
    k = -10; Select[Range[1, 10^7], # + k != 0 && Mod[DivisorSigma[1, #], # + k] == 0 &] (* Vincenzo Librandi, Jul 06 2016 *)
  • PARI
    isok(k) = (k!=10) && !(Mod(sigma(k), k-10)); \\ Michel Marcus, May 30 2025

Extensions

a(19)-a(24) from Giovanni Resta, Jul 06 2016
a(25)-a(26) from Jud McCranie, Dec 02 2019
Terms 6,9 inserted and a(27)-a(29) added by Max Alekseyev, May 30 2025

A274552 Numbers k such that sigma(k) == 0 (mod k-3).

Original entry on oeis.org

2, 4, 5, 6, 7, 8, 15, 52, 315, 592, 1155, 2102272, 815634435
Offset: 1

Views

Author

Paolo P. Lava, Jun 28 2016

Keywords

Examples

			sigma(4) mod (4-3) = 7 mod 1 = 0.

Crossrefs

Contains subsequence A141548.
Cf. A000203, A067702, A087485, A274551, A274553, A274554, A274556, A274557, A274558, A274559, A274560, A274561, A274562, A274563, A274564, A274565, A274566.

Programs

  • Magma
    [n: n in [1..2*10^6] | n ne 3 and SumOfDivisors(n) mod (n-3) eq 0 ]; // Vincenzo Librandi, Jul 02 2016
  • Mathematica
    k = -3; Select[Range[1, 10^6], # + k != 0 && Mod[DivisorSigma[1, #], # + k] == 0 &] (* Michael De Vlieger, Jul 01 2016 *)
  • PARI
    is(n) = if(n == 3, return(0), Mod(sigma(n), n-3)==0) \\ Felix Fröhlich, Jul 02 2016

Extensions

a(12)-a(13) from Giovanni Resta
a(1)=2 inserted by Max Alekseyev, Jun 08 2025

A274556 Numbers k such that sigma(k) == 0 (mod k-5).

Original entry on oeis.org

2, 3, 4, 6, 7, 8, 11, 12, 18, 21, 26, 68, 656, 2336, 8768, 133376, 528896, 34360918016, 35184409837568, 576460757135261696
Offset: 1

Views

Author

Paolo P. Lava, Jun 30 2016

Keywords

Examples

			sigma(6) (mod 6-5) = 12 mod 1 = 0.

Crossrefs

Contains subsequence A101223.
Cf. A067702, A223609, A274551, A274552, A274553, A274554, A274557, A274558, A274559, A274560, A274561, A274562, A274563, A274564, A274565, A274566.

Programs

  • Magma
    [n: n in [1..2*10^6] | n ne 5 and SumOfDivisors(n) mod (n-5) eq 0]; // Vincenzo Librandi, Jul 02 2016
  • Mathematica
    n = -5; Select[Range[1, 10^6], # + n != 0 && Mod[DivisorSigma[1, #], # + n] == 0 &] (* Michael De Vlieger, Jul 01 2016 *)

Extensions

a(18) from Giovanni Resta, Jul 01 2016
Terms 2,3,4 inserted, a(19)-a(20) added by Max Alekseyev, May 25 2025

A274562 Numbers k such that sigma(k) == 0 (mod k-8).

Original entry on oeis.org

5, 6, 7, 9, 10, 11, 12, 14, 17, 38, 92, 168, 170, 248, 752, 988, 2528, 2808, 8648, 12008, 34688, 63248, 117808, 526688, 531968, 820808, 1292768, 1495688, 2095208, 2112512, 3477608, 4495808, 8419328, 12026888, 13192768, 16102808, 26347688, 29322008, 33653888, 169371008, 173631608, 293947648, 537116672, 883927808, 2147975168, 2493705728, 5556840416, 13092865928, 42783299288, 69662739968, 80999455688, 217898810368, 546409576448, 1020401174528, 1081071376208, 1282330216448, 1473186024448, 1577975316488, 1608005456768
Offset: 1

Views

Author

Paolo P. Lava, Jul 05 2016

Keywords

Examples

			sigma(9) mod (9 - 8) = 13 mod 1 = 0.

Crossrefs

Cf. A000203, A045770, A067702, A088833, A181598, A274551, A274552, A274553, A274554, A274556, A274557, A274558, A274559, A274560, A274561, A274563, A274564, A274565, A274566.

Programs

  • Mathematica
    Select[Range[1, 10^6], # - 8 != 0 && Mod[DivisorSigma[1, #], # - 8] == 0 &] (* Michael De Vlieger, Jul 05 2016 *)

Extensions

a(33)-a(59) from Giovanni Resta, Jul 05 2016
Terms 5,6,7 inserted by Max Alekseyev, Jun 04 2025

A274558 Numbers k such that sigma(k) == 0 (mod k-6).

Original entry on oeis.org

5, 7, 13, 14, 20, 30, 45, 76, 630, 688, 2310, 8896, 133888, 537051136, 1631268870, 35184418226176, 144115191028645888, 2305843021024854016
Offset: 1

Views

Author

Paolo P. Lava, Jul 05 2016

Keywords

Comments

Contains terms of A141549, odd terms of A141548 multiplied by 2, and 6 times terms of A191363 coprime to 6. - Max Alekseyev, May 25 2025

Examples

			sigma(7) mod (7-6) = 8 mod 1 = 0.

Crossrefs

Contains subsequence A141549.
Cf. A000203, A045770, A067702, A088833, A141548, A181598, A191363, A274551, A274552, A274553, A274554, A274556, A274557, A274559, A274560, A274561, A274562, A274563, A274564, A274565, A274566.

Programs

  • Mathematica
    Select[Range[7, 10^6],  # - 6 != 0 && Mod[DivisorSigma[1, #], # - 6] == 0 &] (* Michael De Vlieger, Jul 05 2016 *)

Extensions

a(14)-a(15) from Giovanni Resta
Term 5 inserted, a(16)-a(18) added by Max Alekseyev, Jun 04 2025

A274560 Numbers k such that sigma(k) == 0 (mod k-7).

Original entry on oeis.org

3, 5, 6, 8, 10, 11, 15, 27, 34, 72, 232, 34432, 549762629632
Offset: 1

Views

Author

Paolo P. Lava, Jul 05 2016

Keywords

Examples

			sigma(8) mod (8-7) = 15 mod 1 = 0.

Crossrefs

Contains subsequence A141550.
Cf. A000203, A045770, A067702, A088833, A181598, A274551, A274552, A274553, A274554, A274556, A274557, A274558, A274559, A274561, A274562, A274563, A274564, A274565, A274566

Programs

  • Mathematica
    Select[Range[1, 10^6], Mod[DivisorSigma[1, #], # - 7] == 0 &] (* Michael De Vlieger, Jul 05 2016 *)

Extensions

a(13) from Giovanni Resta
Terms 3,5,6 inserted by Max Alekseyev, May 29 2025

A274564 Numbers k such that sigma(k) == 0 (mod k-9).

Original entry on oeis.org

6, 7, 8, 10, 11, 15, 19, 24, 33, 105, 33705, 33624064, 2199041081344
Offset: 1

Views

Author

Paolo P. Lava, Jul 06 2016

Keywords

Examples

			sigma(10) mod (10 - 9) = 18 mod 1 = 0.

Crossrefs

Contains subsequence A223608.
Cf. A045770, A067702, A088833, A181598, A274551, A274552, A274553, A274554, A274556, A274557, A274558, A274559, A274560, A274561, A274562, A274563, A274565, A274566.

Programs

  • Magma
    [n: n in [10..2*10^6] | SumOfDivisors(n) mod (n-9) eq 0 ]; // Vincenzo Librandi, Jul 06 2016
  • Mathematica
    k = -9; Select[Range[Abs@k+1, 10^6], Mod[DivisorSigma[1, #], # + k] == 0 &] (* Vincenzo Librandi, Jul 06 2016 *)
  • PARI
    isok(k) = (k!=9) && (Mod(sigma(k), k-9) == 0); \\ Michel Marcus, May 30 2025

Extensions

a(12)-a(13) from Giovanni Resta, Jul 06 2016
Terms 6,7,8 inserted by Max Alekseyev, May 29 2025

A274559 Numbers k such that sigma(k) == 0 (mod k+7).

Original entry on oeis.org

8, 272, 7232, 30848, 516608, 134094848, 2146992128, 35184309174272
Offset: 1

Views

Author

Paolo P. Lava, Jul 05 2016

Keywords

Examples

			sigma(8) mod (8+7) = 15 mod 15 = 0.

Crossrefs

Contains subsequence A141546.
Cf. A045770, A067702, A088833, A181598, A274551, A274552, A274553, A274554, A274556, A274557, A274558, A274560, A274561, A274562, A274563, A274564, A274565, A274566.

Programs

  • Mathematica
    Select[Range[10^6], Mod[DivisorSigma[1, #], # + 7] == 0 &] (* Michael De Vlieger, Jul 05 2016 *)

Extensions

a(6)-a(7) from Giovanni Resta, Jul 05 2016
a(8) from Max Alekseyev, May 29 2025

A274565 Numbers k such that sigma(k) == 0 (mod k+10).

Original entry on oeis.org

14, 176, 1376, 3230, 3770, 6848, 114256, 125696, 544310, 561824, 740870, 2075648, 4199030, 4607296, 8436950, 33468416, 134045696, 199272950, 624032630, 1113445430, 1550860550, 85905593344, 2199001235456, 35184284008448
Offset: 1

Views

Author

Paolo P. Lava, Jul 06 2016

Keywords

Examples

			sigma(14) mod (14 + 10) = 24 mod 24 = 0.

Crossrefs

Contains subsequence A223611.
Contains 2 * odd terms of A223609.
Cf. A045770, A067702, A088833, A181598, A274551, A274552, A274553, A274554, A274556, A274557, A274558, A274559, A274560, A274561, A274562, A274563, A274564, A274566.

Programs

  • Magma
    [n: n in [1..2*10^6] | SumOfDivisors(n) mod (n+10) eq 0 ]; // Vincenzo Librandi, Jul 06 2016
  • Mathematica
    k = 10; Select[Range[Abs@k+1, 10^6], Mod[DivisorSigma[1, #], # + k] == 0 &] (* Vincenzo Librandi, Jul 06 2016 *)

Extensions

a(13)-a(23) from Giovanni Resta, Jul 06 2016
a(24) from Max Alekseyev, May 29 2025
Showing 1-9 of 9 results.

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

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