A131755 a(n) = floor of the average of distances between consecutive positive divisors of n. Also, a(n) = floor((n-1)/(d(n)-1)), where d(n) = A000005(n).

1, 2, 1, 4, 1, 6, 2, 4, 3, 10, 2, 12, 4, 4, 3, 16, 3, 18, 3, 6, 7, 22, 3, 12, 8, 8, 5, 28, 4, 30, 6, 10, 11, 11, 4, 36, 12, 12, 5, 40, 5, 42, 8, 8, 15, 46, 5, 24, 9, 16, 10, 52, 7, 18, 7, 18, 19, 58, 5, 60, 20, 12, 10, 21, 9, 66, 13, 22, 9, 70, 6, 72, 24, 14, 15, 25, 11, 78, 8

Offset

2,2

Comments

(n-1)/(d(n)-1) is an integer if and only if n is in sequence A096738.

Links

Table of n, a(n) for n=2..80.

Example

The positive divisors of 12 are 1,2,3,4,6,12. The differences between the pairs of consecutive divisors are 2-1=1, 3-2=1, 4-3=1, 6-4=2, 12-6=6. The average of these differences is (1+1+1+2+6)/5 = 11/5. So a(12) = floor(11/5) = 2.

Maple

A131755 := proc(n) local dvs ; dvs := sort(convert(numtheory[divisors](n), list)) ; floor(add(op(i, dvs)-op(i-1, dvs), i=2..nops(dvs))/(nops(dvs)-1)) ; end: seq(A131755(n), n=2..80) ; # R. J. Mathar, Oct 24 2007

Mathematica

Floor/@(Mean[Differences[Divisors[#]]]&/@Range[2, 80]) (* Harvey P. Dale, Dec 13 2016 *)

Crossrefs

Cf. A000005, A096738.

Sequence in context: A074919 A362232 A138009 * A305812 A341857 A292403

Adjacent sequences: A131752 A131753 A131754 * A131756 A131757 A131758

Keyword

nonn

Author

Leroy Quet, Sep 17 2007

Extensions

More terms from R. J. Mathar, Oct 24 2007

Status

approved