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

Author

Benoit Cloitre, Jul 26 2002

Keywords

• easy
• nonn

Comments

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

Links

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

Crossrefs

Subsequence of A087943.

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

Programs

Magma

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

Maple

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

Mathematica

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

PARI

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

Formula

{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