cp's OEIS Frontend

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

%I A067051 #30 Sep 08 2022 08:45:05
%S A067051 2,8,18,32,49,50,72,98,128,162,169,196,200,242,288,338,361,392,441,
%T A067051 450,512,578,648,676,722,784,800,882,961,968,1058,1152,1225,1250,1352,
%U A067051 1369,1444,1458,1521,1568,1682,1764,1800,1849,1922,2048,2178,2312,2450,2592
%N A067051 The smallest k>1 such that k divides sigma(k*n) is equal to 3.
%C A067051 The smallest m>1 such that m divides sigma(m*n) is 2, 3 or 6.
%C A067051 Appears to be the same sequence as A074629. - _Ralf Stephan_, Aug 18 2004. [Proof: Mathar link]
%C A067051 Square terms are in A074216. Nonsquare terms appear to be A001105 except {0}. - _Michel Marcus_, Dec 26 2013
%H A067051 Amiram Eldar, <a href="/A067051/b067051.txt">Table of n, a(n) for n = 1..10000</a>
%H A067051 R. J. Mathar, <a href="/A067051/a067051.pdf">OEIS A074629</a>
%F A067051 {n: A000203(n) mod 6 = 3.}  (Old definition of A074629) - _Labos Elemer_, Aug 26 2002
%F A067051 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
%F A067051 {n: A049605(n) = 3}. - _R. J. Mathar_, May 19 2020
%F A067051 {n: A084301(n) = 3 }. - _R. J. Mathar_, May 19 2020
%F A067051 A087943 INTERSECT A028982. - _R. J. Mathar_, May 30 2020
%p A067051 select(t -> numtheory:-sigma(t) mod 6 = 3, [$1..10000]); # _Robert Israel_, Dec 11 2015
%t A067051 Select[Range@ 2600, Mod[DivisorSigma[1, #], 6] == 3 &] (* _Michael De Vlieger_, Dec 10 2015 *)
%o A067051 (PARI) isok(n) = (sigma(2*n) % 2) && !(sigma(3*n) % 3); \\ _Michel Marcus_, Dec 26 2013
%o A067051 (Magma) [n: n in [1..3*10^3] | (SumOfDivisors(n) mod 6) eq 3]; // _Vincenzo Librandi_, Dec 11 2015
%Y A067051 Subsequence of A087943.
%Y A067051 Cf. A072862, A074384, A074627, A074628, A074630.
%K A067051 easy,nonn
%O A067051 1,1
%A A067051 _Benoit Cloitre_, Jul 26 2002