

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[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, 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



