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A128863
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a(0)=1. For n >= 1, a(n) = number of positive divisors of (n+a(n-1)).
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2
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1, 2, 3, 4, 4, 3, 3, 4, 6, 4, 4, 4, 5, 6, 6, 4, 6, 2, 6, 3, 2, 2, 8, 2, 4, 2, 6, 4, 6, 4, 4, 4, 9, 8, 8, 2, 4, 2, 8, 2, 8, 3, 6, 3, 2, 2, 10, 4, 6, 4, 8, 2, 8, 2, 8, 6, 4, 2, 12, 2, 4, 4, 8, 2, 8, 2, 6, 2, 8, 4, 4, 6, 8, 5, 2, 4, 10, 4, 4, 2, 4, 4, 4, 4, 8, 4, 12, 6, 4, 4, 4, 4, 12, 8, 8, 2, 6, 2, 9, 12, 10, 4
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OFFSET
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0,2
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COMMENTS
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Starting the sequence at a(1)=1 instead and using the recursion to get all terms after this, gets the sequence beginning: 1,2,2,4,3,3,4,6,4,4,4,5,... The sequences are the same from term a(4) on, whether starting with a(0)=1 or with a(1)=1.
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LINKS
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EXAMPLE
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a(11)+12 = 16. So a(12) is the number of positive divisors of 16, which is 5.
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MAPLE
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with(numtheory): a:=proc(n) if n=0 then 1 else tau(n+a(n-1)) fi end: seq(a(n), n=0..130); # Emeric Deutsch, Apr 26 2007
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MATHEMATICA
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nxt[{n_, a_}]:={n+1, DivisorSigma[0, a+n+1]}; NestList[nxt, {0, 1}, 110][[All, 2]] (* Harvey P. Dale, Mar 12 2019 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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