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 A067051 The smallest k>1 such that k divides sigma(k*n) is equal to 3. 10
 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 (list; graph; refs; listen; history; text; internal format)
 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: A063581 A293296 A055044 * A074629 A209303 A001105 Adjacent sequences:  A067048 A067049 A067050 * A067052 A067053 A067054 KEYWORD easy,nonn AUTHOR Benoit Cloitre, Jul 26 2002 STATUS approved

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Last modified June 15 15:16 EDT 2021. Contains 345049 sequences. (Running on oeis4.)