

A131755


a(n) = floor of the average of distances between consecutive positive divisors of n. Also, a(n) = floor((n1)/(d(n)1)), where d(n) = A000005(n).


1



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
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OFFSET

2,2


COMMENTS

(n1)/(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 21=1, 32=1, 43=1, 64=2, 126=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(i1, 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: A060794 A074919 A138009 * A292403 A271773 A277127
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



