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A125741
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The ratio of A117731(n) and A082687(n) when they are different.
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2
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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
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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FORMULA
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EXAMPLE
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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,...}.
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MATHEMATICA
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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} ]
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CROSSREFS
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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} ].
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KEYWORD
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hard,nonn
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AUTHOR
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STATUS
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approved
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