A077087 -id:A077087 - cp's OEIS frontend

A217791 Numbers k such that sigma(k) = 3*sigma(k+1).

180, 12000, 30996, 47940, 66780, 102816, 128040, 234300, 494088, 712272, 1133088, 1408212, 1623072, 1692768, 1896336, 1925196, 2024760, 2388720, 2529090, 2836008, 3423120, 3724320, 3822360, 4628760, 4750920, 7219608, 7359912, 7603488, 7749060

Offset: 1

Paolo P. Lava, Mar 25 2013

nonn

			47940 is in the sequence because sigma(47940)=145152, sigma(47941)=48384, and 145152=3*48384.
7749060 is in the sequence because sigma(7749060)=24192000, sigma(7749061)=8064000, and 24192000=3*8064000.

Donovan Johnson, Table of n, a(n) for n = 1..500

Cf. A000203, A002961, A058073, A067081, A077087, A163193, A272027 (3*sigma(n)).

[n: n in [1..10^7] | SumOfDivisors(n) eq 3*SumOfDivisors(n+1)]; // Bruno Berselli, Mar 25 2013

A217791:=proc(q) local n;
for n from 1 to q do if sigma(n)=3*sigma(n+1) then print(n); fi; od; end:
A217791(10^10);

Position[Partition[DivisorSigma[1,Range[78*10^5]],2,1],?(#[[1]] == 3#[[2]]&), {1},Heads->False]//Flatten (* _Harvey P. Dale, Oct 17 2016 *)

More terms from Bruno Berselli, Mar 25 2013

A340713 Numbers k such that sigma(k+1) = 4 * sigma(k).

Original entry on oeis.org

37033919, 141162839, 264995639, 596672999, 606523679, 630777839, 791656319, 920424119, 1060332839, 1379454719, 1954690919, 3799661039, 4024838999, 4633959959, 5393988599, 5935994063, 8831231639, 9866482079, 11237657759, 11273710139, 12266364599, 14440498379, 14952625379

Offset: 1

Seiichi Manyama, Jan 17 2021

nonn

Seiichi Manyama, Table of n, a(n) for n = 1..40 (using A058072 data)

Cf. A000203, A002961, A058072, A067081, A077087, A340715.

isok(k) = sigma(k+1) == 4*sigma(k); \\ Michel Marcus, Jan 18 2021

a(10)-a(23) from Seiichi Manyama using A058072 data, Jan 17 2021

A340715 Least positive number k such that sigma(k+1) = n * sigma(k).

Original entry on oeis.org

14, 5, 1, 37033919, 14182439039

Offset: 1

Seiichi Manyama, Jan 17 2021

			  n | sigma(a(n)) | sigma(a(n)+1)
----+-------------+--------------
  1 |          24 |            24
  2 |           6 |            12
  3 |           1 |             3
  4 |    39940992 |     159763968
  5 | 14182439040 |   70912195200

Cf. A000203, A002961, A058072, A067081, A077087, A080371, A340713, A340720.

k = 1;n = 1;Print[While[DivisorSigma[1, k + 1] != n*DivisorSigma[1, k], k;k k+]; k] (* Robert P. P. McKone, Jan 17 2021 *)

{a(n) = my(k=1); while(sigma(k+1)!=n*sigma(k), k++); k}

A077089 Quotients when sigma(k+1)/sigma(k) is an integer.

Original entry on oeis.org

3, 2, 1, 2, 1, 1, 2, 1, 1, 1, 2, 3, 1, 3, 1, 2, 1, 2, 2, 3, 2, 1, 1, 1, 1, 1, 3, 1, 1, 1, 2, 2, 2, 2, 3, 1, 2, 2, 3, 2, 2, 1, 2, 1, 2, 1, 1, 1, 1, 2, 3, 2, 2, 1, 2, 2, 1, 2, 3, 3, 1, 3, 1, 2, 2, 2, 3, 2, 1, 1, 3, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 1, 3, 3, 2, 1, 2, 1, 2, 2, 3, 1, 2, 2, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1

Offset: 1

Labos Elemer, Oct 31 2002

nonn

			a(1) = sigma(2)/sigma(1) = 3/1 = 3.
a(2) = sigma(6)/sigma(5) = 12/6 = 2.
a(3) = sigma(15)/sigma(14) = 24/24 = 1.

Amiram Eldar, Table of n, a(n) for n = 1..5000 (terms 1..500 from Seiichi Manyama)

Cf. A000203, A002961, A058072, A067081, A077086, A077087.

Do[s=Mod[a=DivisorSigma[1, n+1], b=DivisorSigma[1, n]]; If[Equal[s, 0], Print[a/b]], {n, 1, 10000000}]
Select[#[[2]]/#[[1]]&/@Partition[DivisorSigma[1,Range[10^6]],2,1], IntegerQ] (* Harvey P. Dale, Dec 26 2015 *)

a(n) = sigma(A058072(n)+1)/sigma(A058072(n)). - Seiichi Manyama, Jan 16 2021

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A217791 Numbers k such that sigma(k) = 3*sigma(k+1).

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A340713 Numbers k such that sigma(k+1) = 4 * sigma(k).

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A340715 Least positive number k such that sigma(k+1) = n * sigma(k).

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A077089 Quotients when sigma(k+1)/sigma(k) is an integer.

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