

A087943


Numbers n such that 3 divides sigma(n).


5



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


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*p3)^(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.
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



