A354859 a(n) is the numerator of 1/prime(n) + 2/prime(n-1) + 3/prime(n-2) + ... + (n-1)/3 + n/2.

1, 4, 71, 124, 11111, 92402, 257189, 43708274, 2344987003, 1855369084, 2729707472269, 11281836318542, 1705853427969059, 120757830191824486, 1124815045783478971, 118422287191742563724, 1291008724583331399881, 113743044027018860349034, 70575236921156825443680027, 8002471039307070610187173702

Offset: 1

Author

Ilya Gutkovskiy, Jun 09 2022

Keywords

• nonn
• frac

Comments

Numerator of a second order prime harmonic number.

Examples

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

Crossrefs

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

Programs

Mathematica

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

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

Formula

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