%I #21 Jan 06 2023 06:33:30

%S 7,5,7,31,7,5,7,21,7,5,7,31,7,5,7,127,7,5,7,31,7,5,7,21,7,5,7,31,7,5,

%T 7,85,7,5,7,31,7,5,7,21,7,5,7,31,7,5,7,127,7,5,7,31,7,5,7,21,7,5,7,31,

%U 7,5,7,511,7,5,7,31,7,5,7,21,7,5,7,31,7,5,7,127,7,5,7,31,7,5,7,21,7,5,7,31

%N Numerator of sigma(4n)/sigma(n).

%H Antti Karttunen, <a href="/A088839/b088839.txt">Table of n, a(n) for n = 1..16384</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>.

%F a(n) = (8*A006519(n)-1)/(1+2*A096268(n)). - _Robert Israel_, Nov 19 2017

%F From _Amiram Eldar_, Jan 06 2023: (Start)

%F a(n) = numerator(A193553(n)/A000203(n)).

%F Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k)/A088840(k) = 3*A065442 + 1 = 5.820085... . (End)

%p f:= proc(n) local m;

%p m:= padic:-ordp(n,2);

%p if m::odd then (2^(m+3)-1)/3 else 2^(m+3)-1 fi

%p end proc:

%p map(f, [$1..200]); # _Robert Israel_, Nov 19 2017

%t k=4; Table[Numerator[DivisorSigma[1, k*n]/DivisorSigma[1, n]], {n, 1, 128}]

%o (PARI) A088839(n) = numerator(sigma(4*n)/sigma(n)); \\ _Antti Karttunen_, Nov 18 2017

%Y For denominator see A088840.

%Y Cf. A000203, A038712, A088837, A088838, A088841, A080278, A193553.

%Y Cf. A006519, A065442, A096268.

%K easy,nonn,frac

%O 1,1

%A _Labos Elemer_, Nov 04 2003

%E Typo in definition corrected by _Antti Karttunen_, Nov 18 2017