A049605 -id:A049605 - cp's OEIS frontend

A067051 The smallest k>1 such that k divides sigma(k*n) is equal to 3.

2, 8, 18, 32, 49, 50, 72, 98, 128, 162, 169, 196, 200, 242, 288, 338, 361, 392, 441, 450, 512, 578, 648, 676, 722, 784, 800, 882, 961, 968, 1058, 1152, 1225, 1250, 1352, 1369, 1444, 1458, 1521, 1568, 1682, 1764, 1800, 1849, 1922, 2048, 2178, 2312, 2450, 2592

Offset: 1

Benoit Cloitre, Jul 26 2002

The smallest m>1 such that m divides sigma(m*n) is 2, 3 or 6.
Appears to be the same sequence as A074629. - Ralf Stephan, Aug 18 2004. [Proof: Mathar link]
Square terms are in A074216. Nonsquare terms appear to be A001105 except {0}. - Michel Marcus, Dec 26 2013

Amiram Eldar, Table of n, a(n) for n = 1..10000
R. J. Mathar, OEIS A074629

Subsequence of A087943.

Cf. A072862, A074384, A074627, A074628, A074630.

[n: n in [1..3*10^3] | (SumOfDivisors(n) mod 6) eq 3]; // Vincenzo Librandi, Dec 11 2015

select(t -> numtheory:-sigma(t) mod 6 = 3, [$1..10000]); # Robert Israel, Dec 11 2015

Select[Range@ 2600, Mod[DivisorSigma[1, #], 6] == 3 &] (* Michael De Vlieger, Dec 10 2015 *)

isok(n) = (sigma(2*n) % 2) && !(sigma(3*n) % 3); \\ Michel Marcus, Dec 26 2013

{n: A000203(n) mod 6 = 3.}  (Old definition of A074629) - Labos Elemer, Aug 26 2002
In the prime factorization of n, no odd prime has odd exponent, and 2 has odd exponent or at least one prime == 1 (mod 6) has exponent == 2 (mod 6). - Robert Israel, Dec 11 2015
{n: A049605(n) = 3}. - R. J. Mathar, May 19 2020
{n: A084301(n) = 3 }. - R. J. Mathar, May 19 2020
A087943 INTERSECT A028982. - R. J. Mathar, May 30 2020

A072862 The smallest k>1 such that k divides sigma(k*n) is equal to 6.

Original entry on oeis.org

1, 4, 9, 16, 25, 36, 64, 81, 100, 121, 144, 225, 256, 289, 324, 400, 484, 529, 576, 625, 729, 841, 900, 1024, 1089, 1156, 1296, 1600, 1681, 1936, 2025, 2116, 2209, 2304, 2401, 2500, 2601, 2809, 2916, 3025, 3364, 3481, 3600, 4096, 4356, 4624, 4761, 5041

Offset: 1

Benoit Cloitre, Jul 26 2002

The smallest k>1 such that k divides sigma(k*n) is always 2, 3 or 6. Sequence generates squares but not all the squares (49, 169, 196, 361, 441, 676, 784, ... are the first squares not in the sequence).

This is not the sequence of solutions to sigma(n) == 1 (mod 6), because 2401 is in this sequence but sigma(2401) == 5 (mod 6). See A074384 for more examples. - R. J. Mathar, May 19 2020

{n: A049605(n) = 6}. - R. J. Mathar, May 19 2020

A072864 Numbers m such that the smallest k dividing sigma(k*m^2) is equal to 3.

Original entry on oeis.org

7, 13, 14, 19, 21, 26, 28, 31, 35, 37, 38, 39, 42, 43, 52, 56, 57, 61, 62, 63, 65, 67, 70, 73, 74, 76, 77, 78, 79, 84, 86, 91, 93, 95, 97, 103, 104, 105, 109, 111, 112, 114, 117, 119, 122, 124, 126, 127, 129, 130, 133, 134, 139, 140, 143, 146, 148, 151, 152, 154

Offset: 1

Benoit Cloitre, Jul 27 2002

Sequence contains primes of the form 6x+1 (A002476) and multiples of those primes, except (6x+1)^2. If x is not in the sequence, the smallest k dividing sigma(k*x^2) is equal to 6.

Cf. A049605.

isok(n) = A049605(n^2) != 6; \\ Michel Marcus, Nov 21 2013

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A067051 The smallest k>1 such that k divides sigma(k*n) is equal to 3.

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A072862 The smallest k>1 such that k divides sigma(k*n) is equal to 6.

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A072864 Numbers m such that the smallest k dividing sigma(k*m^2) is equal to 3.

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