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%I #25 Jan 09 2021 21:04:50
%S 0,1,4,8,15,9,21,13,28,41,23,11,39,25,49,73,42,24,63,43,85,53,17,41,
%T 101,70,112,72,16,46,118,86,149,197,143,95,186,148,88,32,122,80,176,
%U 132,48,126,54,6,130,187,94,22,120,66,186,114,234,154,64,124,292,230,134,30,157,241,97,29,155
%N a(0) = 0, a(1) = 1; for n > 1, a(n) = a(n-1) - sigma(n) if nonnegative and not already in the sequence, otherwise a(n) = a(n-1) + sigma(n), where sigma(n) is the sum of the 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 sum of the divisors of n is used. See A000203.
%C For the first 10 million terms the smallest value not appearing is 76. It is likely that all values are eventually visited, although this is unknown.
%C In the same range the maximum value is a(9297600) = 93571073, and 402979 terms repeat a previously visited value, the first time this occurs is a(23) = a(9) = 41. The longest run of consecutive increasing terms is 5, starting at a(105187) = 25833, while the longest run of consecutive decreasing terms is 7, starting at a(6826248) = 83016261.
%e a(2) = 4. As sigma(2) = 3, and a(1)<3, a(2) = a(1) + 3 = 4.
%e a(4) = 15. As sigma(4) = 7, and 1 has previously appeared, a(4) = a(3) + 7 = 15.
%e a(5) = 9. As sigma(5) = 6, and 9 has not previously appeared, a(5) = a(4) - 6 = 9.
%Y Cf. A005132, A000203, A335372, A336760, A336761, A000040.
%K nonn
%O 0,3
%A _Scott R. Shannon_, Aug 16 2020
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