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 A098464 Numbers k such that lcm(1,2,3,...,k) equals the denominator of the k-th harmonic number H(k). 17
 1, 2, 3, 4, 5, 9, 10, 11, 12, 13, 14, 15, 16, 17, 27, 28, 29, 30, 31, 32, 49, 50, 51, 52, 53, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Numbers k such that A110566(k) = 1. Shiu (2016) conjectured that this sequence is infinite. - Amiram Eldar, Feb 02 2021 LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 Peter Shiu, The denominators of harmonic numbers, arXiv:1607.02863 [math.NT], 2016. Eric Weisstein's World of Mathematics, Harmonic Number. MATHEMATICA Select[Range[250], LCM@@Range[ # ]==Denominator[HarmonicNumber[ # ]]&] PROG (PARI) isok(n) = lcm(vector(n, i, i)) == denominator(sum(i=1, n, 1/i)); \\ Michel Marcus, Mar 07 2018 (Python) from fractions import Fraction from sympy import lcm k, l, h, A098464_list = 1, 1, Fraction(1, 1), [] while k < 10**6:     if l == h.denominator:         A098464_list.append(k)     k += 1     l = lcm(l, k)     h += Fraction(1, k) # Chai Wah Wu, Mar 07 2021 CROSSREFS Cf. A002805 (denominator of H(n)), A003418 (lcm(1, 2, ..., n)), A110566. Sequence in context: A265335 A179223 A069117 * A068586 A068585 A037472 Adjacent sequences:  A098461 A098462 A098463 * A098465 A098466 A098467 KEYWORD easy,nonn AUTHOR T. D. Noe, Sep 09 2004 STATUS approved

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Last modified May 8 22:05 EDT 2021. Contains 343668 sequences. (Running on oeis4.)