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A136180
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a(n) = Sum_{k=1..d(n)-1} gcd(b(k), b(k+1)), where b(k) is the k-th positive divisor of n and d(n) is the number of positive divisors of n.
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4
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0, 1, 1, 3, 1, 5, 1, 7, 4, 7, 1, 11, 1, 9, 7, 15, 1, 17, 1, 19, 9, 13, 1, 23, 6, 15, 13, 25, 1, 26, 1, 31, 13, 19, 9, 35, 1, 21, 15, 37, 1, 41, 1, 37, 21, 25, 1, 47, 8, 37, 19, 43, 1, 53, 13, 49, 21, 31, 1, 57, 1, 33, 27, 63, 15, 61, 1, 55, 25, 48, 1, 71, 1, 39, 37, 61, 13, 71, 1, 73, 40
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OFFSET
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1,4
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COMMENTS
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a(n) is the sum of the terms in row n of A136178.
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LINKS
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EXAMPLE
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The positive divisors of 20 are 1,2,4,5,10,20; gcd(1,2)=1, gcd(2,4)=2, gcd(4,5)=1, gcd(5,10)=5, and gcd(10,20)=10, so a(20) = 1+2+1+5+10 = 19.
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MAPLE
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with(numtheory): a:=proc(n) local div: div:=divisors(n): add(gcd(div[k], div[k+1]), k=1..tau(n)-1) end proc: seq(a(n), n=1..70); # Emeric Deutsch, Jan 08 2008
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MATHEMATICA
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Array[Total@ Map[GCD @@ # &, Partition[#, 2, 1] &@ Divisors@ #] &, 81] (* Michael De Vlieger, Oct 16 2017 *)
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PROG
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(PARI) a(n) = my(d=divisors(n)); vecsum(vector(#d-1, k, gcd(d[k], d[k+1]))); \\ Michel Marcus, Oct 16 2017
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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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