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Numerator of Sum_{i=2..t} (d(i)/d(i-1)-1), where d(1), ..., d(t) are the divisors of n.
3

%I #12 Sep 07 2018 04:41:00

%S 0,1,2,2,4,5,6,3,4,7,10,10,12,9,14,4,16,4,18,17,16,13,22,25,8,15,6,19,

%T 28,68,30,5,20,19,42,14,36,21,22,51,40,31,42,23,92,25,46,5,12,6,26,25,

%U 52,11,46,79,28,31,58,157,60,33,146,6,48,35,66,29,32,218,70,131,72,39,22,31,88

%N Numerator of Sum_{i=2..t} (d(i)/d(i-1)-1), where d(1), ..., d(t) are the divisors of n.

%H Antti Karttunen, <a href="/A085085/b085085.txt">Table of n, a(n) for n = 1..65537</a>

%H M. D. Vose, <a href="http://dx.doi.org/10.1016/0022-314X(84)90107-0">Integers with consecutive divisors in small ratio</a>, J. Number Theory, 19 (1984), 233-238.

%e 0, 1, 2, 2, 4, 5/2, 6, 3, 4, 7/2, 10, 10/3, 12, 9/2, 14/3, ...

%p with(numtheory): f := proc(n) local t1,t2,t3,i; t1 := divisors(n); t3 := convert(t1,list); t2 := 0; for i from 2 to nops(t3) do t2 := t2+(t3[i]/t3[i-1]-1); od; t2; end;

%o (PARI) a(n) = {my(d = divisors(n)); numerator(sum(i=2, #d, d[i]/d[i-1] - 1));} \\ _Michel Marcus_, Feb 25 2015

%Y Cf. A085091.

%K nonn,frac

%O 1,3

%A _N. J. A. Sloane_, Aug 11 2003