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 A125741 The ratio of A117731(n) and A082687(n) when they are different. 2
 7, 13, 7, 7, 37, 19, 119, 41, 31, 37, 37, 43, 13, 7, 13, 49, 7, 7, 61, 71, 103, 67, 73, 139, 17, 79, 19, 29, 97, 103, 223, 109, 37, 359, 7, 49, 7, 127, 953, 7, 139, 41, 151, 1627, 157, 797, 179, 13, 163, 13, 13, 13, 13, 13, 31, 31, 181, 193, 199, 919, 193, 211, 757, 37 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Corresponding numbers n such that A117731(n) differs from A082687(n) are listed in A125740(n) = {14, 52, 98, 105, 111, 114, 119, 164, 310, 444, 518, 602, 676, 686, 715, 735, 749, 833, ...}. a(n) divides A125740(n). Most a(n) are primes. The first composite term in a(n) is a(7) = 119 = 7*17. a(n) is composite for n = {7, 16, 36}. a(16) = a(36) = 49 = 7^2. LINKS FORMULA a(n) = A117731[ A125740(n) ] / A082687[ A125740(n) ]. EXAMPLE A082687(n) begins {1, 7, 37, 533, 1627, 18107, 237371, 95549, 1632341, 155685007, 156188887, 3602044091, 18051406831, 7751493599, ...}. Thus a(1) = 7 because A117731(n)/A082687(n) = {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1,...}. MATHEMATICA h=0; Do[ h=h+1/(n+1)/(2n+1); f=Numerator[n*h]; g=Numerator[h]; If[ !Equal[f, g], Print[ {n, f/g} ] ], {n, 1, 10000} ] CROSSREFS Cf. A125740 = numbers n such that A117731(n) differs from A082687(n). Cf. A117731 = Numerator of n*Sum[ 1/(n+k), {k, 1, n} ]. Cf. A082687 = Numerator of Sum[ 1/(n+k), {k, 1, n} ]. Sequence in context: A225091 A225516 A134039 * A103705 A157517 A164929 Adjacent sequences:  A125738 A125739 A125740 * A125742 A125743 A125744 KEYWORD hard,nonn AUTHOR Alexander Adamchuk, Dec 04 2006 STATUS approved

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Last modified September 25 19:55 EDT 2020. Contains 337344 sequences. (Running on oeis4.)