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A126563 Numbers n such that the ratio of A117731(n) and A082687(n) is composite. 0
119, 735, 5145, 36015 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(1) = 7*17, a(2) = 3*5*7^2, a(3) = 3*5*7^3. Corresponding composite terms in A125741(n) are {119, 49, 49,...}. A125741(n) is composite for n = {7, 16, 36, ...}. A125741(n) = {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, ...} The ratio of A117731(n) and A082687(n) when they are different. A082687(n) = Numerator of the 2n-th alternating harmonic number H'(2n) = Sum ((-1)^(k+1)/k, k=1..2n). H'(2n) = H(2n) - H(n), where H(n) = Sum (1/k, k=1..n) is n-th Harmonic Number. A117731(n) = Numerator of the sum of all matrix elements of n X n Hilbert Matrix M(i,j) = 1/(i+j-1), (i,j=1..n).

LINKS

Table of n, a(n) for n=1..4.

Eric Weisstein, The World of Mathematics: Hilbert Matrix.

Eric Weisstein, The World of Mathematics: Harmonic Number

MATHEMATICA

h=0; Do[ h=h+1/(n+1)/(2n+1); f=Numerator[n*h]; g=Numerator[h]; If[ !Equal[f, g] && !PrimeQ[f/g], Print[ {n, f/g, FactorInteger[n], FactorInteger[f/g]} ] ], {n, 1, 10000} ]

CROSSREFS

Cf. A117731 = Numerator of n*Sum[ 1/(n+k), {k, 1, n} ]. Cf. A082687 = Numerator of Sum[ 1/(n+k), {k, 1, n} ]. Cf. A125740 = numbers n such that A117731(n) differs from A082687(n). Cf. A125741 = The ratio of A117731(n) and A082687(n) when they are different. Cf. A126196, A126197, A125581 = numbers n such that n does not divide the denominator of the n-th harmonic number nor the denominator of the n-th alternating harmonic number.

Sequence in context: A256907 A049226 A106572 * A067134 A156930 A263128

Adjacent sequences:  A126560 A126561 A126562 * A126564 A126565 A126566

KEYWORD

bref,hard,more,nonn

AUTHOR

Alexander Adamchuk, Mar 12 2007, Jun 09 2007

STATUS

approved

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Last modified February 20 13:33 EST 2019. Contains 320327 sequences. (Running on oeis4.)