A358787 a(1)=1; let x=gcd(a(n-1),n); for n > 1, a(n) = a(n-1) + n if x=1 or a(n-1)/x=1, otherwise a(n) = a(n-1)/x.
1, 3, 6, 3, 8, 4, 11, 19, 28, 14, 25, 37, 50, 25, 5, 21, 38, 19, 38, 19, 40, 20, 43, 67, 92, 46, 73, 101, 130, 13, 44, 11, 44, 22, 57, 19, 56, 28, 67, 107, 148, 74, 117, 161, 206, 103, 150, 25, 74, 37, 88, 22, 75, 25, 5, 61, 118, 59, 118, 59, 120, 60, 20, 5, 70, 35, 102, 3, 72, 36
Offset: 1
Keywords
Examples
For n=2, gcd(2,1)=1 so a(2) = 2+1 = 3. For n=3, gcd(3,3)=3=a(2) so a(3) = 3+3 = 6. For n=4, gcd(4,6)=2 so a(4) = 6/2 = 3.
Links
- Michael De Vlieger, Log log scatterplot of a(n), n = 1..2^20.
- Michael De Vlieger, Log log scatterplot of a(n), n = 1..2^16, with x = gcd(a(n-1), n), showing x=1 or a(n-1)/x = 1 in red, else dark blue.
Programs
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Mathematica
nn = 2^16; a[1] = 1; Do[g = GCD[a[n - 1], n]; If[Or[g == 1, Set[k, a[n - 1]/g] == 1], a[n] = a[n - 1] + n, a[n] = k], {n, 2, nn}]; Array[a, nn] (* Michael De Vlieger, Dec 13 2022 *) -
Python
from math import gcd from itertools import count, islice def agen(): # generator of terms an = 1 for n in count(2): yield an x = gcd(an, n) an = an + n if x == 1 or x == an else an//x print(list(islice(agen(), 70))) # Michael S. Branicky, Dec 15 2022