A375522 a(n) is the denominator of Sum_{k = 1..n} 1 / (k*A375781(k)).

2, 6, 15, 105, 1155, 1336335, 892896284280, 398631887241408183843480, 19863422690705846097977473796903171171326157280, 14091270035344566960604487534521565339065390839583445590118556137472614250693240040301050080

Offset

1,1

Comments

Let S(n) = Sum_{k = 1..n} 1 / (k*A375781(k)) = S1(n)/S2(n) when reduced to lowest terms, where S1(n) = A375521(n), S2(n) = the present sequence.

The differences S2(n) - S1(n) are surprisingly small: for n = 1,2,...,34 the values S2(n) - S1(n) are:

1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

suggesting the conjecture that they are always 1 except for n = 4 and 6 (compare the Theorem in A374983).

Links

Table of n, a(n) for n=1..10.

Example

The first few fractions are 1/2, 5/6, 14/15, 103/105, 1154/1155, 1336333/1336335, 892896284279/892896284280, ...

Prog

(Python)
from itertools import islice
from math import gcd
from sympy import nextprime
def A375522_gen(): # generator of terms
    p, q, k = 0, 1, 1
    while (k:=nextprime(k)):
        m=q//(k*(q-p))+1
        p, q = p*k*m+q, k*m*q
        p //= (r:=gcd(p, q))
        q //= r
        yield q
A375522_list = list(islice(A375522_gen(), 11)) # Chai Wah Wu, Aug 30 2024

Crossrefs

Cf. A375781, A375521.

Sequence in context: A078328 A038111 A356803 * A376051 A261726 A302775

Adjacent sequences: A375519 A375520 A375521 * A375523 A375524 A375525

Keyword

nonn,frac

Author

Rémy Sigrist and N. J. A. Sloane, Aug 30 2024

Status

approved