
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 2nth 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 nth Harmonic Number. A117731(n) = Numerator of the sum of all matrix elements of n X n Hilbert Matrix M(i,j) = 1/(i+j1), (i,j=1..n).


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 nth harmonic number nor the denominator of the nth alternating harmonic number.
Sequence in context: A256907 A049226 A106572 * A067134 A156930 A263128
Adjacent sequences: A126560 A126561 A126562 * A126564 A126565 A126566
