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A087943
Numbers n such that 3 divides sigma(n).
14
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
Sequence in context: A176590 A253061 A320730 * A034020 A187476 A121411
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