A163193 -id:A163193 - 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

A340720 Least positive number k such that sigma(k) = n * sigma(k+1).

Original entry on oeis.org

14, 12, 180, 25908120

Offset: 1

Seiichi Manyama, Jan 17 2021

			  n | sigma(a(n)) | sigma(a(n)+1)
----+-------------+--------------
  1 |          24 |            24
  2 |          28 |            14
  3 |         546 |           182
  4 |   103680000 |      25920000

Cf. A002961, A080372, A163193, A217791, A340715.

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

A340582 Numbers k such that sigma(k) = 4 * sigma(k+1).

Original entry on oeis.org

25908120, 136616760, 171430560, 196876680, 354049920, 405601560, 514374840, 825473880, 1204476000, 2223650520, 2510539920, 3003191100, 4017339480, 4574146500, 6129062940, 6797728800, 7311296520, 9779952000, 12472435080, 13103164800, 19989450000, 22180840920, 22710872520

Offset: 1

Seiichi Manyama, Jan 21 2021

nonn

Seiichi Manyama, Table of n, a(n) for n = 1..30 (using A058073 data)

Cf. A002961, A080372, A163193, A217791, A340713, A340720.

a(9)-a(23) from Seiichi Manyama using A058073 data, Jan 21 2021

A353034 Numbers m such that tau(m) = 2 * tau(m + 1) and simultaneously sigma(m) = 2 * sigma(m + 1), where tau(k) = A000005(k) and sigma(k) = A000203(k).

Original entry on oeis.org

20118, 20712, 79338, 103410, 203898, 267630, 570342, 907710, 1093026, 1228062, 1263918, 1663752, 2322760, 3268782, 3468486, 3527250, 5483418, 6277038, 6500442, 7637980, 9181578, 9297078, 17708178, 18638646, 25274946, 25364526, 25768302, 25909254, 31118664

Offset: 1

Jaroslav Krizek, Apr 18 2022

nonn

Corresponding values of tau(m): 16, 16, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 32, ...

Corresponding values of sigma(m): 46080, 51840, 181440, 276480, 432000, 701568, 1200960, 2211840, ...

			tau(20118) = 16 = 2 * tau(20119) = 2 * 8, sigma(20118) = 46080 = 2 * sigma(20119) = 2 * 23040.

Cf. A000005 (tau), A000203 (sigma), A054004, A347603, A353033.

Subsequence of A163193.

[m: m in [2..10^6] | #Divisors(m) eq 2 * #Divisors(m + 1) and &+Divisors(m) eq 2 * &+Divisors(m + 1)]

cp's OEIS Frontend

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

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A340720 Least positive number k such that sigma(k) = n * sigma(k+1).

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A340582 Numbers k such that sigma(k) = 4 * sigma(k+1).

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A353034 Numbers m such that tau(m) = 2 * tau(m + 1) and simultaneously sigma(m) = 2 * sigma(m + 1), where tau(k) = A000005(k) and sigma(k) = A000203(k).

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