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a(n) is the denominator of 1/prime(n) + 2/prime(n-1) + 3/prime(n-2) + ... + (n-1)/3 + n/2.
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%I #6 Jun 09 2022 17:18:58

%S 2,3,30,35,2310,15015,34034,4849845,223092870,154040315,200560490130,

%T 742073813481,101416754509070,6541380665835015,55899071144408310,

%U 5431526412865007455,54936010004406075402,4511091590746421960895,2619440517026755685293030,278970415063349480483707695

%N a(n) is the denominator of 1/prime(n) + 2/prime(n-1) + 3/prime(n-2) + ... + (n-1)/3 + n/2.

%C Denominator of a second order prime harmonic number.

%F a(n) is the denominator of Sum_{j=1..n} Sum_{i=1..j} 1/prime(i).

%e 1/2, 4/3, 71/30, 124/35, 11111/2310, 92402/15015, 257189/34034, ...

%t Table[Sum[(n - k + 1)/Prime[k], {k, 1, n}], {n, 1, 20}] // Denominator

%o (Python)

%o from fractions import Fraction

%o from sympy import prime, primerange

%o def a(n): return sum(Fraction(n-i, p) for i, p in enumerate(primerange(1, prime(n)+1))).denominator

%o print([a(n) for n in range(1, 21)]) # _Michael S. Branicky_, Jun 09 2022

%Y Cf. A002110, A027611, A354859 (numerators).

%K nonn,frac

%O 1,1

%A _Ilya Gutkovskiy_, Jun 09 2022