cp's OEIS Frontend

A196736 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.

%I A196736 #19 Mar 01 2020 06:34:52
%S A196736 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 A196736 43,45,47,49,51,53,59,61,63,64,65,67,71,73,75,77,79,81,83,87,89,91,95,
%U A196736 97,99,101,103,107,109,113,119,121,123,125,127
%N A196736 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 A196736 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 A196736 (Sage)
%o A196736 def is_A196736(n): # inefficient, for reference purposes
%o A196736     k = lambda x: sum(1 for m in (1..n) if number_of_divisors(gcd(n,m))==x)
%o A196736     cototient_n = n-euler_phi(n)
%o A196736     z = number_of_divisors(cototient_n) if cototient_n > 0 else 0
%o A196736     v = [(n-sum(k(i) for i in (1..j))) for j in (1..z)]
%o A196736     return len(set(v)) == len(v) and all(vi.divides(cototient_n) for vi in v)
%o A196736 # _D. S. McNeil_, Oct 14 2011
%K A196736 nonn
%O A196736 1,2
%A A196736 _Naohiro Nomoto_, Oct 06 2011