A339571 A133058 with duplicates removed.

1, 4, 8, 2, 12, 3, 24, 16, 21, 7, 27, 48, 32, 30, 15, 5, 34, 64, 36, 18, 54, 41, 80, 120, 45, 59, 104, 150, 75, 123, 91, 142, 194, 97, 151, 206, 262, 131, 189, 248, 308, 77, 139, 202, 266, 133, 199, 334, 167, 237, 380, 95, 169, 244, 320, 158, 79, 82, 164, 86

Offset: 1

Author

N. J. A. Sloane, Dec 09 2020

Keywords

• nonn

Links

• Dana G. Korssjoen, Biyao Li, Stefan Steinerberger, Raghavendra Tripathi, and Ruimin Zhang, Finding structure in sequences of real numbers via graph theory: a problem list, arXiv:2012.04625 [math.CO], Dec 08, 2020. See Section 2.6.

Crossrefs

Cf. A133058.

Programs

Mathematica

DeleteDuplicates@ Block[{a = {1, 1}, k = 1}, Do[AppendTo[a, If[# == 1, a[[-1]] + i + 1, a[[-1]]/#]] &@ GCD[a[[-1]], i], {i, 2, 80}]; a] (* Michael De Vlieger, Dec 09 2020 *)

PARI

lista(nn) = my(v=List([1]), x=1, y); print1(1); for(n=2, nn, if(!setsearch(Set(v), x=if(1==y=gcd(x, n), x+n+1, x/y)), print1(", ", x); listput(v, x))); \\ Jinyuan Wang, Dec 12 2020

Python

from math import gcd
from itertools import count, islice
def A339571_gen(): # generator of terms
    a, aset = 1, {1}
    yield 1
    for n in count(2):
        a = a+n+1 if (b:=gcd(a,n)) == 1 else a//b
        if a not in aset:
            aset.add(a)
            yield a
A339571_list = list(islice(A339571_gen(),30)) # Chai Wah Wu, Mar 18 2023

Extensions

More terms from Jinyuan Wang, Dec 12 2020