A361470 a(n) = gcd(n+1, A135504(n)).

1, 3, 2, 1, 6, 1, 8, 9, 2, 1, 12, 1, 14, 3, 16, 1, 18, 1, 20, 21, 2, 1, 24, 5, 2, 27, 28, 1, 30, 1, 32, 3, 2, 35, 36, 1, 38, 3, 40, 1, 42, 1, 44, 45, 2, 1, 48, 49, 50, 3, 4, 1, 54, 55, 56, 57, 2, 1, 60, 1, 62, 63, 64, 5, 66, 1, 68, 3, 70, 1, 72, 1, 74, 75, 76, 77, 6, 1, 80, 81, 2, 1, 84, 85, 2, 3, 88

Offset: 1

Author

Antti Karttunen, Mar 26 2023

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A135504, A135506.

Programs

Mathematica

MapIndexed[GCD[First[#2] + 1, #1] &, RecurrenceTable[{a[1] == 1, a[n] == a[n - 1] + LCM[a[n - 1], n]}, a, {n, 87}] ] (* Michael De Vlieger, May 11 2023 *)

PARI

up_to = 65537;
A361470list(up_to_n) = { my(v=vector(up_to), x1=1, x2); for(n=2, 1+up_to_n, x2 = x1+lcm(x1, n); v[n-1] = gcd(x1,n); x1=x2); (v); };
v361470 = A361470list(up_to);
A361470(n) = v361470[n];

Python

from math import gcd
from itertools import count, islice
def A361470_gen(): # generator of terms
    x = 1
    for n in count(2):
        yield (y:=gcd(x,n))
        x += x*n//y
A361470_list = list(islice(A361470_gen(),20)) # Chai Wah Wu, May 11 2023

Formula

a(n) = (n+1) / A135506(n).