cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A099377 Numerators of the harmonic means of the divisors of the positive integers.

This page as a plain text file.
%I A099377 #22 Feb 16 2025 08:32:55
%S A099377 1,4,3,12,5,2,7,32,27,20,11,18,13,7,5,80,17,36,19,20,21,22,23,16,75,
%T A099377 52,27,3,29,10,31,64,11,68,35,324,37,38,39,32,41,7,43,22,45,23,47,120,
%U A099377 49,100,17,156,53,18,55,56,57,116,59,30,61,31,189,448,65,11,67,68,23,35
%N A099377 Numerators of the harmonic means of the divisors of the positive integers.
%H A099377 Ivan Neretin, <a href="/A099377/b099377.txt">Table of n, a(n) for n = 1..10000</a>
%H A099377 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/OresConjecture.html">Ore's Conjecture</a>
%e A099377 1, 4/3, 3/2, 12/7, 5/3, 2, 7/4, 32/15, ...
%t A099377 f[n_] := DivisorSigma[0, n]/Plus @@ (1/Divisors@n); Numerator@ Array[f, 70] (* _Robert G. Wilson v_, Aug 04 2010 *)
%t A099377 Table[Numerator[DivisorSigma[0, n]/DivisorSigma[-1, n]], {n, 70}] (* _Ivan Neretin_, Nov 13 2016 *)
%o A099377 (PARI) a(n) = my(d=divisors(n)); numerator(#d/sum(k=1, #d, 1/d[k])); \\ _Michel Marcus_, Nov 13 2016
%o A099377 (Python)
%o A099377 from sympy import gcd, divisor_sigma
%o A099377 def A099377(n): return (lambda x, y: y*n//gcd(x,y*n))(divisor_sigma(n),divisor_sigma(n,0)) # _Chai Wah Wu_, Oct 20 2021
%Y A099377 Cf. A099378.
%K A099377 nonn,frac
%O A099377 1,2
%A A099377 _Eric W. Weisstein_, Oct 13 2004
%E A099377 More terms from _Robert G. Wilson v_, Aug 04 2010