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.

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

Michael De Vlieger, Table of n, a(n) for n = 1..10000

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

Cf. A136178, A136179, A136183.

Sequence in context: A118402 A122383 A292393 * A095112 A160596 A092319

Adjacent sequences: A136177 A136178 A136179 * A136181 A136182 A136183

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