A354860 a(n) is the denominator of 1/prime(n) + 2/prime(n-1) + 3/prime(n-2) + ... + (n-1)/3 + n/2.

2, 3, 30, 35, 2310, 15015, 34034, 4849845, 223092870, 154040315, 200560490130, 742073813481, 101416754509070, 6541380665835015, 55899071144408310, 5431526412865007455, 54936010004406075402, 4511091590746421960895, 2619440517026755685293030, 278970415063349480483707695

Offset: 1

Author

Ilya Gutkovskiy, Jun 09 2022

Keywords

• nonn
• frac

Comments

Denominator of a second order prime harmonic number.

Examples

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

Crossrefs

Cf. A002110, A027611, A354859 (numerators).

Programs

Mathematica

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

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))).denominator
print([a(n) for n in range(1, 21)]) # Michael S. Branicky, Jun 09 2022

Formula

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