A074629 -id:A074629 - 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

A074628 Numbers k such that sigma(k) == 2 mod 6.

Original entry on oeis.org

7, 13, 19, 21, 28, 31, 37, 39, 43, 52, 57, 61, 63, 67, 73, 76, 79, 84, 93, 97, 103, 109, 111, 112, 117, 124, 127, 129, 139, 148, 151, 156, 157, 163, 171, 172, 175, 181, 183, 189, 193, 199, 201, 208, 211, 219, 223, 228, 229, 237, 241, 244, 252

Offset: 1

Labos Elemer, Aug 26 2002

			For k=39: sigma(39) = 1+3+13+39 = 56 = 6*9 + 2.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A000203, A072862, A074384, A074627, A074628, A074629, A074630.

Select[Range[300],Mod[DivisorSigma[1,#],6]==2&] (* Harvey P. Dale, Nov 14 2014 *)

isok(n) = ((sigma(n) % 6) == 2); \\ Michel Marcus, Dec 19 2013

A000203(n) mod 6 = 2.

{n: A084301(n) = 2}. - R. J. Mathar, May 19 2020

A097022 a(n) = (sigma(2n^2)-3)/6.

Original entry on oeis.org

0, 2, 6, 10, 15, 32, 28, 42, 60, 77, 66, 136, 91, 142, 201, 170, 153, 302, 190, 325, 370, 332, 276, 552, 390, 457, 546, 598, 435, 1007, 496, 682, 864, 767, 883, 1270, 703, 952, 1189, 1317, 861, 1852, 946, 1396, 1875, 1382, 1128, 2216, 1400, 1952, 1995, 1921

Offset: 1

Labos Elemer, Aug 24 2004

nonn

See A065764, A065765 and A097022.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A065764, A065765, A000203, A001105, A002117, A072682, A074627, A074628, A074629, A074630, A067051.

Table[(DivisorSigma[1,2n^2]-3)/6,{n,60}] (* Harvey P. Dale, Sep 12 2022 *)

a(n) = (sigma(2*n^2) - 3)/6; \\ Michel Marcus, Dec 20 2013

a(n) = (A065765(n)-3)/6 = A000203(A001105(n) - 3)/6.

Sum_{k=1..n} a(k) ~ c * n^3, where c = 4*zeta(3)/Pi^2 = 0.243587... . - Amiram Eldar, Oct 28 2022

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

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A074628 Numbers k such that sigma(k) == 2 mod 6.

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A097022 a(n) = (sigma(2n^2)-3)/6.

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