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A091259 Numerator of sigma_3(n)/sigma(n).

%I A091259 #33 Aug 28 2024 01:06:04
%S A091259 1,3,7,73,21,21,43,39,757,63,111,73,157,129,147,151,273,2271,343,219,
%T A091259 301,333,507,273,15751,471,511,3139,813,441,931,4161,777,819,903,
%U A091259 55261,1333,1029,1099,819,1641,903,1807,8103,15897,1521,2163,1057,39331,47253
%N A091259 Numerator of sigma_3(n)/sigma(n).
%H A091259 Robert Israel, <a href="/A091259/b091259.txt">Table of n, a(n) for n = 1..10000</a>
%F A091259 a(p) = A002061(p), for prime p. - _Robert Israel_, Jan 25 2018
%F A091259 Sum_{k=1..n} a(k)/A091258(k) ~ c * n^3, where c = (Pi^2/18)*zeta(3)^2 * Product_{p prime} (1 - 2/p^2 - 1/p^3 + 5/p^5 - 3/p^6) = 0.2382648075... . - _Amiram Eldar_, Nov 21 2022
%F A091259 Conjecture: a(n) (mod 3) = A353816(n). - _Michel Marcus_, Aug 11 2024
%p A091259 seq(numer(numtheory:-sigma[3](n)/numtheory:-sigma(n)),n=1..100); # _Robert Israel_, Jan 25 2018
%t A091259 Array[Numerator[DivisorSigma[3,#]/DivisorSigma[1,#]]&,50] (* _Harvey P. Dale_, Feb 29 2016 *)
%o A091259 (PARI) a(n) = numerator(sigma(n, 3)/sigma(n)); \\ _Michel Marcus_, Jan 26 2018
%o A091259 (Magma) [Numerator(DivisorSigma(3,n)/DivisorSigma(1,n)): n in [1..50]]; // _Vincenzo Librandi_, Jan 26 2018
%Y A091259 Cf. A001158, A000203, A002061, A002117, A086463, A091258 (denominators), A091260.
%Y A091259 Cf. A032766.
%K A091259 easy,nonn,frac,look
%O A091259 1,2
%A A091259 _Labos Elemer_, Feb 12 2004