A104076 If k(m) is the m-th divisor (when the divisors are ordered by size) of n, then a(n) = gcd(k(1)+k(2), k(2)+k(3), k(3)+k(4), ..., k(j-1)+k(j)), where j is the number of divisors of n.

3, 4, 3, 6, 1, 8, 3, 4, 1, 12, 1, 14, 3, 4, 3, 18, 1, 20, 3, 2, 1, 24, 1, 6, 3, 4, 1, 30, 1, 32, 3, 2, 1, 6, 1, 38, 3, 4, 1, 42, 1, 44, 3, 2, 1, 48, 1, 8, 1, 4, 1, 54, 1, 2, 1, 2, 1, 60, 1, 62, 3, 2, 3, 6, 1, 68, 3, 2, 1, 72, 1, 74, 3, 4, 1, 2, 1, 80, 1, 4, 1, 84, 1, 2, 3, 4, 1, 90, 1, 4, 3, 2, 1, 6, 1, 98

Offset: 2

Author

Leroy Quet, Aug 31 2008

Keywords

• nonn

Examples

			The divisors of 14 are 1,2,7,14. So a(14) = gcd(1+2, 2+7, 7+14) = 3.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 2..1000

Crossrefs

Cf. A143771.

Programs

Maple

A104076 := proc(n) local dvs ; dvs := sort(convert(numtheory[divisors](n),list)) ; igcd(seq( op(i,dvs)+op(i+1,dvs), i=1..nops(dvs)-1)) ; end: for n from 2 to 140 do printf("%d,",A104076(n)) ; od: # R. J. Mathar, Sep 05 2008

Mathematica

Table[GCD@@(Total/@Partition[Divisors[n],2,1]),{n,2,100}] (* Harvey P. Dale, Dec 18 2018 *)

Extensions

Extended by R. J. Mathar, Sep 05 2008

Definition corrected by Leroy Quet, Sep 21 2008