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a(n) is the numerator of 1/prime(n) + 2/prime(n-1) + 3/prime(n-2) + ... + (n-1)/3 + n/2.
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%I #7 Jun 09 2022 17:18:40

%S 1,4,71,124,11111,92402,257189,43708274,2344987003,1855369084,

%T 2729707472269,11281836318542,1705853427969059,120757830191824486,

%U 1124815045783478971,118422287191742563724,1291008724583331399881,113743044027018860349034,70575236921156825443680027,8002471039307070610187173702

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

%C Numerator of a second order prime harmonic number.

%F a(n) is the numerator 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}] // Numerator

%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))).numerator

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

%Y Cf. A024451, A027612, A120272, A354860 (denominators).

%K nonn,frac

%O 1,2

%A _Ilya Gutkovskiy_, Jun 09 2022