A394372 a(1)=1, a(2)=2, a(3)=3; for n > 3, a(n) = a(n-1) + gcd(n, a(n-2) * a(n-3)).

1, 2, 3, 5, 6, 9, 10, 12, 21, 31, 32, 35, 36, 50, 65, 73, 74, 75, 76, 86, 89, 91, 92, 93, 94, 96, 99, 103, 104, 107, 108, 116, 119, 121, 128, 129, 130, 132, 171, 211, 212, 215, 216, 220, 265, 267, 268, 271, 272, 274, 291, 295, 296, 299, 304, 312, 331, 333, 334, 337

Offset

1,2

Links

Table of n, a(n) for n=1..60.

Mathematica

a[n_] := a[n] = If[n < 4, n, a[n-1] + GCD[n, a[n-2]*a[n-3]]]; Array[a, 100] (* Amiram Eldar, Apr 17 2026 *)

Prog

(Python)
import math
def a(n):
    if n == 1: return 1
    if n == 2: return 2
    if n == 3: return 3
    x, y, z = 1, 2, 3
    for i in range(4, n+1):
        x, y, z = y, z, z + math.gcd(i, y * x)
    return z
print([a(n) for n in range(1, 61)])

Crossrefs

Sequence in context: A029451 A029455 A234718 * A341158 A294849 A320226

Adjacent sequences: A394369 A394370 A394371 * A394373 A394374 A394375

Keyword

nonn,easy

Author

Wang Yixiang, Apr 17 2026

Status

approved