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A158274
Numerators of antiharmonic means of divisors of n.
3
1, 5, 5, 3, 13, 25, 25, 17, 7, 65, 61, 15, 85, 125, 65, 11, 145, 35, 181, 13, 125, 305, 265, 85, 21, 425, 41, 75, 421, 325, 481, 65, 305, 725, 325, 21, 685, 181, 425, 221, 841, 625, 925, 61, 91, 1325, 1105, 55, 43, 35
OFFSET
1,2
COMMENTS
Numbers k such that sigma_2(k)/sigma_1(k) = A001157(k)/A000203(k) are integers are in A020487.
LINKS
FORMULA
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)).
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
EXAMPLE
Antiharmonic means of divisors of n>=1: 1, 5/3, 5/2, 3, 13/2, 25/6, ...
MATHEMATICA
Table[Numerator[DivisorSigma[2, n]/DivisorSigma[1, n]], {n, 50}] (* Ivan Neretin, May 22 2015 *)
PROG
(PARI) a(n) = numerator(sigma(n, 2)/sigma(n)); \\ Amiram Eldar, Nov 21 2022
CROSSREFS
Cf. A000203, A001157, A020487, A065473, A152649, A158275 (denominators)
Sequence in context: A225666 A365078 A175505 * A202695 A110986 A193721
KEYWORD
nonn,frac
AUTHOR
Jaroslav Krizek, Mar 15 2009
STATUS
approved