Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #23 May 30 2020 10:28:24
%S 2,5,6,8,10,11,14,15,17,18,20,22,23,24,26,29,30,32,33,34,35,38,40,41,
%T 42,44,45,46,47,49,50,51,53,54,55,56,58,59,60,62,65,66,68,69,70,71,72,
%U 74,77,78,80,82,83,85,86,87,88,89,90,92,94,95,96,98,99,101,102,104,105,106
%N Numbers n such that 3 divides sigma(n).
%C 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
%H Enrique Pérez Herrero, <a href="/A087943/b087943.txt">Table of n, a(n) for n = 1..5000</a>
%F a(n) << n^k for any k > 1, where << is the Vinogradov symbol. - _Charles R Greathouse IV_, Sep 04 2013
%F 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
%F 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
%p select(n -> numtheory:-sigma(n) mod 3 = 0, [$1..1000]); # _Robert Israel_, Nov 09 2016
%t Select[Range[1000],Mod[DivisorSigma[1,#],3]==0&] (* _Enrique Pérez Herrero_, Sep 03 2013 *)
%o (PARI) is(n)=sigma(n)%3==0 \\ _Charles R Greathouse IV_, Sep 04 2013
%o (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
%Y Cf. A000203, A059269, A066498, A034020, A028983, A074216, A329963 (complement).
%K nonn
%O 1,1
%A Yuval Dekel (dekelyuval(AT)hotmail.com), Oct 27 2003
%E More terms from _Benoit Cloitre_ and _Ray Chandler_, Oct 27 2003