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

1,1

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

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

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 *)

Prog

(PARI) isok(n) = (sigma(2*n) % 2) && !(sigma(3*n) % 3); \\ Michel Marcus, Dec 26 2013
(Magma) [n: n in [1..3*10^3] | (SumOfDivisors(n) mod 6) eq 3]; // Vincenzo Librandi, Dec 11 2015

Crossrefs

Subsequence of A087943.

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

Sequence in context: A055044 A356209 A357851 * A074629 A209303 A001105

Adjacent sequences: A067048 A067049 A067050 * A067052 A067053 A067054

Keyword

easy,nonn

Author

Benoit Cloitre, Jul 26 2002

Status

approved