[seqfan] Re: cototient divisibility in A196736

D. S. McNeil dsm054 at gmail.com
Fri Oct 14 02:39:29 CEST 2011

> Where is the error?

I don't think there is one.  However, I think I can reproduce the
terms in the sequence if I impose the distinctness condition in the
comment that "n - ( Sum_{i=1..j} k(i) ) are all distinct divisors";
note that 6 and 10 both have cototient sets with duplicate 1s.

IOW, this seems to match the terms:

def is_A196736(n):
    k = lambda x: sum(1 for m in (1..n) if number_of_divisors(gcd(n,m))==x)
    cototient_n = n-euler_phi(n)
    z = number_of_divisors(cototient_n) if cototient_n > 0 else 0
    v = [(n-sum(k(i) for i in (1..j))) for j in (1..z)]
    return len(set(v)) == len(v) and all(vi.divides(cototient_n) for vi in v)

Probably the name should be tweaked.


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