A196736 - OEIS

%I #19 Mar 01 2020 06:34:52

%S 1,2,3,4,5,7,8,9,11,12,13,15,16,17,19,23,25,27,29,31,32,33,35,37,41,

%T 43,45,47,49,51,53,59,61,63,64,65,67,71,73,75,77,79,81,83,87,89,91,95,

%U 97,99,101,103,107,109,113,119,121,123,125,127

%N Define k(x) = number of m such that A000005(gcd(n,m)) is x where m runs from 1 to n , x = 1,2,.. ; z = A000005( cototient(n) ) ; sequence gives numbers n such that n - ( Sum_{i=1..j} k(i) ) divides cototient(n) for any j <= z , k(i)>0.

%C Sequence gives numbers n such that n - ( Sum_{i=1..j} k(i) ) are all distinct divisors of cototient(n) for all j <= z.

%o (Sage)

%o def is_A196736(n): # inefficient, for reference purposes

%o     k = lambda x: sum(1 for m in (1..n) if number_of_divisors(gcd(n,m))==x)

%o     cototient_n = n-euler_phi(n)

%o     z = number_of_divisors(cototient_n) if cototient_n > 0 else 0

%o     v = [(n-sum(k(i) for i in (1..j))) for j in (1..z)]

%o     return len(set(v)) == len(v) and all(vi.divides(cototient_n) for vi in v)

%o # _D. S. McNeil_, Oct 14 2011

%K nonn

%O 1,2

%A _Naohiro Nomoto_, Oct 06 2011