A158274 - OEIS

%I #14 Nov 21 2022 09:39:00

%S 1,5,5,3,13,25,25,17,7,65,61,15,85,125,65,11,145,35,181,13,125,305,

%T 265,85,21,425,41,75,421,325,481,65,305,725,325,21,685,181,425,221,

%U 841,625,925,61,91,1325,1105,55,43,35

%N Numerators of antiharmonic means of divisors of n.

%C Numbers k such that sigma_2(k)/sigma_1(k) = A001157(k)/A000203(k) are integers are in A020487.

%H Ivan Neretin, <a href="/A158274/b158274.txt">Table of n, a(n) for n = 1..10000</a>

%F Antiharmonic mean of divisors of number n = Product (p_i^e_i) is sigma_2(n)/sigma_1(n) = A001157(n)/A000203(n) = Product ((p_i^(e_i+1)+1)/(p_i+1)).

%F Sum_{k=1..n} a(k)/A158275(k) ~ c * n^2, where c = (Pi^4/72) * Product_{p prime} (1 - (3*p-2)/(p^3)) = A152649 * A065473 = 0.387941... . - _Amiram Eldar_, Nov 21 2022

%e Antiharmonic means of divisors of n>=1: 1, 5/3, 5/2, 3, 13/2, 25/6, ...

%t Table[Numerator[DivisorSigma[2, n]/DivisorSigma[1, n]], {n, 50}] (* _Ivan Neretin_, May 22 2015 *)

%o (PARI) a(n) = numerator(sigma(n,2)/sigma(n)); \\ _Amiram Eldar_, Nov 21 2022

%Y Cf. A000203, A001157, A020487, A065473, A152649, A158275 (denominators)

%K nonn,frac

%O 1,2

%A _Jaroslav Krizek_, Mar 15 2009