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A136180
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.
4
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
OFFSET
1,4
COMMENTS
a(n) is the sum of the terms in row n of A136178.
LINKS
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.
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, Jan 08 2008
MATHEMATICA
Array[Total@ Map[GCD @@ # &, Partition[#, 2, 1] &@ Divisors@ #] &, 81] (* Michael De Vlieger, Oct 16 2017 *)
PROG
(PARI) a(n) = my(d=divisors(n)); vecsum(vector(#d-1, k, gcd(d[k], d[k+1]))); \\ Michel Marcus, Oct 16 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Leroy Quet, Dec 19 2007
EXTENSIONS
More terms from Emeric Deutsch, Jan 08 2008
Terms beyond a(70) from R. J. Mathar, Feb 27 2010
STATUS
approved