A085085 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

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.

EXAMPLE

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

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;

PROG

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

CROSSREFS

Cf. A085091.

Sequence in context: A261665 A208096 A049269 * A121600 A126870 A364049

Adjacent sequences: A085082 A085083 A085084 * A085086 A085087 A085088

KEYWORD

nonn,frac

AUTHOR

N. J. A. Sloane, Aug 11 2003

STATUS

approved