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 A087943 Numbers n such that 3 divides sigma(n). 11
 2, 5, 6, 8, 10, 11, 14, 15, 17, 18, 20, 22, 23, 24, 26, 29, 30, 32, 33, 34, 35, 38, 40, 41, 42, 44, 45, 46, 47, 49, 50, 51, 53, 54, 55, 56, 58, 59, 60, 62, 65, 66, 68, 69, 70, 71, 72, 74, 77, 78, 80, 82, 83, 85, 86, 87, 88, 89, 90, 92, 94, 95, 96, 98, 99, 101, 102, 104, 105, 106 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Numbers n such that in the prime factorization n = Product_i p_i^e_i, there is some p_i == 1 (mod 3) with e_i == 2 (mod 3) or some p_i == 2 (mod 3) with e_i odd. - Robert Israel, Nov 09 2016 LINKS Enrique Pérez Herrero, Table of n, a(n) for n = 1..5000 FORMULA a(n) << n^k for any k > 1, where << is the Vinogradov symbol. - Charles R Greathouse IV, Sep 04 2013 a(n) ~ n as n -> infinity: since Sum_{primes p == 2 (mod 3)} 1/p diverges, asymptotically almost every number is divisible by some prime p == 2 (mod 3) but not by p^2. - Robert Israel, Nov 09 2016 Because sigma(n) and sigma(3n)=A144613(n) differ by a multiple of 3, these are also the numbers n such that n divides sigma(3n). - R. J. Mathar, May 19 2020 MAPLE select(n -> numtheory:-sigma(n) mod 3 = 0, [\$1..1000]); # Robert Israel, Nov 09 2016 MATHEMATICA Select[Range, Mod[DivisorSigma[1, #], 3]==0&] (* Enrique Pérez Herrero, Sep 03 2013 *) PROG (PARI) is(n)=sigma(n)%3==0 \\ Charles R Greathouse IV, Sep 04 2013 (PARI) is(n)=forprime(p=2, 997, my(e=valuation(n, p)); if(e && Mod(p, 3*p-3)^(e+1)==1, return(1), n/=p^e)); sigma(n)%3==0 \\ Charles R Greathouse IV, Sep 04 2013 CROSSREFS Cf. A000203, A059269, A066498, A034020, A028983, A074216, A329963 (complement). Sequence in context: A176590 A253061 A320730 * A034020 A187476 A121411 Adjacent sequences:  A087940 A087941 A087942 * A087944 A087945 A087946 KEYWORD nonn AUTHOR Yuval Dekel (dekelyuval(AT)hotmail.com), Oct 27 2003 EXTENSIONS More terms from Benoit Cloitre and Ray Chandler, Oct 27 2003 STATUS approved

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Last modified June 15 22:06 EDT 2021. Contains 345053 sequences. (Running on oeis4.)