A085085 Numerator of Sum_{i=2..t} (d(i)/d(i-1)-1), where d(1), ..., d(t) are the divisors of n.

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

Offset: 1

Author

N. J. A. Sloane, Aug 11 2003

Keywords

• nonn
• frac

Examples

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

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• M. D. Vose, Integers with consecutive divisors in small ratio, J. Number Theory, 19 (1984), 233-238.

Crossrefs

Cf. A085091.

Programs

Maple

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;

PARI

a(n) = {my(d = divisors(n)); numerator(sum(i=2, #d, d[i]/d[i-1] - 1));} \\ Michel Marcus, Feb 25 2015