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Gozinta Chains

Published on Sunday, 21st February 2016, 07:00 am; Solved by 489;
Difficulty rating: 35%

Problem 548

A gozinta chain for n is a sequence {1,a,b,...,n} where each element properly divides the next.
There are eight gozinta chains for 12:
{1,12} ,{1,2,12}, {1,2,4,12}, {1,2,6,12}, {1,3,12}, {1,3,6,12}, {1,4,12} and {1,6,12}.
Let g(n) be the number of gozinta chains for n, so g(12)=8.
g(48)=48 and g(120)=132.

Find the sum of the numbers n not exceeding 1016 for which g(n)=n.