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 A099378 Denominators of the harmonic means of the divisors of the positive integers. 46
 1, 3, 2, 7, 3, 1, 4, 15, 13, 9, 6, 7, 7, 3, 2, 31, 9, 13, 10, 7, 8, 9, 12, 5, 31, 21, 10, 1, 15, 3, 16, 21, 4, 27, 12, 91, 19, 15, 14, 9, 21, 2, 22, 7, 13, 9, 24, 31, 19, 31, 6, 49, 27, 5, 18, 15, 20, 45, 30, 7, 31, 12, 52, 127, 21, 3, 34, 21, 8, 9, 36, 65, 37, 57, 62, 35, 24, 7, 40, 93 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Ivan Neretin, Table of n, a(n) for n = 1..10000 Eric Weisstein's World of Mathematics, Ore's Conjecture EXAMPLE 1, 4/3, 3/2, 12/7, 5/3, 2, 7/4, 32/15, ... MATHEMATICA f[n_] := DivisorSigma[0, n]/Plus @@ (1/Divisors@n); Denominator@ Array[f, 80] (* Robert G. Wilson v, Aug 04 2010 *) Table[Denominator[DivisorSigma[0, n]/DivisorSigma[-1, n]], {n, 80}] (* Ivan Neretin, Nov 13 2016 *) PROG (PARI) a(n) = my(d=divisors(n)); denominator(#d/sum(k=1, #d, 1/d[k])); \\ Michel Marcus, Nov 13 2016 (PARI) first(n)=my(v=vector(n)); forfactored(k=1, n, v[k[1]]=denominator(sigma(k, 0)/sigma(k, -1))); v \\ Charles R Greathouse IV, Nov 01 2021 (Python) from sympy import gcd, divisor_sigma def A099378(n): return (lambda x, y: x//gcd(x, y*n))(divisor_sigma(n), divisor_sigma(n, 0)) # Chai Wah Wu, Oct 20 2021 CROSSREFS Cf. A099377. Sequence in context: A245601 A355934 A296513 * A182885 A182891 A071190 Adjacent sequences: A099375 A099376 A099377 * A099379 A099380 A099381 KEYWORD nonn,frac AUTHOR Eric W. Weisstein, Oct 13 2004 EXTENSIONS More terms from Robert G. Wilson v, Aug 04 2010 STATUS approved

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Last modified May 26 07:52 EDT 2024. Contains 372807 sequences. (Running on oeis4.)