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A136180
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a(n) = sum{k=1 to d(n)-1) GCD(b(k),b(k+1)), where b(k) is the k-th positive divisor of n and d(n) = the number of positive divisors of n.
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3
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| a(n) = the sum of the terms in row n of A136178.
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EXAMPLE
| 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
| 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 (deutsch(AT)duke.poly.edu), Jan 08 2008
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CROSSREFS
| Cf. A136178, A136179, A136183.
Sequence in context: A147088 A118402 A122383 * A095112 A160596 A092319
Adjacent sequences: A136177 A136178 A136179 * A136181 A136182 A136183
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KEYWORD
| nonn
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AUTHOR
| Leroy Quet Dec 19 2007
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EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 08 2008
Terms beyond a(70) from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 27 2010
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