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 A284650 Denominator of sum of reciprocals of all divisors of all positive integers <= n. 3
 1, 2, 6, 12, 60, 60, 420, 840, 2520, 504, 5544, 5544, 72072, 72072, 360360, 720720, 12252240, 12252240, 232792560, 232792560, 232792560, 232792560, 5354228880, 5354228880, 26771144400, 26771144400, 80313433200, 80313433200, 2329089562800 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Amiram Eldar, Table of n, a(n) for n = 1..1000 FORMULA G.f.: (1/(1 - x))*Sum_{k>=1} log(1/(1 - x^k)) (for A284648(n)/a(n), see example). a(n) = denominator of Sum_{k=1..n} Sum_{d|k} 1/d. a(n) = denominator of Sum_{k=1..n} sigma(k)/k. EXAMPLE 1, 5/2, 23/6, 67/12, 407/60, 527/60, 4169/420, 9913/840, 33379/2520, 7583/504, 89461/5544, 102397/5544, 1408777/72072, 1532329/72072, 8238221/360360, ... MATHEMATICA Table[Denominator[Sum[DivisorSigma[-1, k], {k, 1, n}]], {n, 1, 29}] Table[Denominator[Sum[DivisorSigma[1, k]/k, {k, 1, n}]], {n, 1, 29}] nmax = 29; Rest[Denominator[CoefficientList[Series[1/(1 - x) Sum[Log[1/(1 - x^k)], {k, 1, nmax}], {x, 0, nmax}], x]]] PROG (PARI) for(n=1, 29, print1(denominator(sum(k=1, n, sigma(k)/k)), ", ")) \\ Indranil Ghosh, Mar 31 2017 (Python) from sympy import divisor_sigma, Integer print([sum(divisor_sigma(k)/Integer(k) for k in range(1, n + 1)).denominator() for n in range(1, 30)]) # Indranil Ghosh, Mar 31 2017 CROSSREFS Cf. A000203, A017665, A017666, A108775, A284648 (numerators). Sequence in context: A341617 A083268 A225628 * A085911 A211418 A058312 Adjacent sequences: A284647 A284648 A284649 * A284651 A284652 A284653 KEYWORD nonn,frac AUTHOR Ilya Gutkovskiy, Mar 31 2017 STATUS approved

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Last modified March 29 21:39 EDT 2023. Contains 361599 sequences. (Running on oeis4.)