A087943 Numbers n such that 3 divides sigma(n).

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

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[1000], 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