A336760 - OEIS

A336760

a(0) = 0; for n > 0, a(n) = a(n-1) - tau(n) if nonnegative and not already in the sequence, otherwise a(n) = a(n-1) + tau(n), where tau(n) is the number of divisors of n.

%I #21 Jan 09 2021 21:05:06

%S 0,1,3,5,2,4,8,6,10,7,11,9,15,13,17,21,16,14,20,18,12,16,20,22,30,27,

%T 23,19,25,27,35,33,39,43,47,51,42,40,36,32,24,26,34,36,42,48,44,46,56,

%U 53,59,55,49,51,59,63,71,67,71,69,57,59,63,69,62,58,50,52,58,54,62,60,72,70,66,72

%N a(0) = 0; for n > 0, a(n) = a(n-1) - tau(n) if nonnegative and not already in the sequence, otherwise a(n) = a(n-1) + tau(n), where tau(n) is the number of divisors of n.

%C This sequences uses the same rules as Recamán's sequence A005132 except that, instead of adding or subtracting n each term, the number of divisors of n is used. See A000005.

%C For the first 10 million terms the smallest value not appearing is 28. The data indicate that a(n)/n approaches 1 as n goes to infinity. As tau(n) <= 2*sqrt(n) (see A046522), it implies that 28 and other small unvisited values will never be visited.

%C In the same range the maximum value is a(9998226) = 10987569, and 2202001 terms repeat a previously visited value, the first time this occurs is a(21) = a(16) = 16. The longest run of consecutive increasing terms is 30, starting at a(1115610) = 1217112, while the longest run of consecutive decreasing terms is 534, starting at a(9960335) = 10946233.

%H <a href="/index/Rea#Recaman">Index entries for sequences related to Recamán's sequence</a>.

%e a(2) = 3. As 2 has two divisors, a(2) = a(1) + 2 = 1 + 2 = 3.

%e a(4) = 2. As 4 has three divisors, and as 2 has not been previously visited and is nonnegative, a(4) = a(3) - 3 = 5 - 3 = 2.

%Y Cf. A005132, A000005, A046522, A336761.

%K nonn

%O 0,3

%A _Scott R. Shannon_, Aug 03 2020