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 A354859 a(n) is the numerator of 1/prime(n) + 2/prime(n-1) + 3/prime(n-2) + ... + (n-1)/3 + n/2. 2
 1, 4, 71, 124, 11111, 92402, 257189, 43708274, 2344987003, 1855369084, 2729707472269, 11281836318542, 1705853427969059, 120757830191824486, 1124815045783478971, 118422287191742563724, 1291008724583331399881, 113743044027018860349034, 70575236921156825443680027, 8002471039307070610187173702 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Numerator of a second order prime harmonic number. LINKS Table of n, a(n) for n=1..20. FORMULA a(n) is the numerator of Sum_{j=1..n} Sum_{i=1..j} 1/prime(i). EXAMPLE 1/2, 4/3, 71/30, 124/35, 11111/2310, 92402/15015, 257189/34034, ... MATHEMATICA Table[Sum[(n - k + 1)/Prime[k], {k, 1, n}], {n, 1, 20}] // Numerator PROG (Python) from fractions import Fraction from sympy import prime, primerange def a(n): return sum(Fraction(n-i, p) for i, p in enumerate(primerange(1, prime(n)+1))).numerator print([a(n) for n in range(1, 21)]) # Michael S. Branicky, Jun 09 2022 CROSSREFS Cf. A024451, A027612, A120272, A354860 (denominators). Sequence in context: A367523 A162135 A047939 * A088693 A322397 A333543 Adjacent sequences: A354856 A354857 A354858 * A354860 A354861 A354862 KEYWORD nonn,frac AUTHOR Ilya Gutkovskiy, Jun 09 2022 STATUS approved

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Last modified September 13 16:28 EDT 2024. Contains 375910 sequences. (Running on oeis4.)