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%I #11 Dec 13 2016 10:20:06
%S 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,
%T 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,
%U 19,58,5,60,20,12,10,21,9,66,13,22,9,70,6,72,24,14,15,25,11,78,8
%N 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).
%C (n-1)/(d(n)-1) is an integer if and only if n is in sequence A096738.
%e 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.
%p 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
%t Floor/@(Mean[Differences[Divisors[#]]]&/@Range[2,80]) (* _Harvey P. Dale_, Dec 13 2016 *)
%Y Cf. A000005, A096738.
%K nonn
%O 2,2
%A _Leroy Quet_, Sep 17 2007
%E More terms from _R. J. Mathar_, Oct 24 2007
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