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.

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, 43, 45, 47, 49, 51, 53, 59, 61, 63, 64, 65, 67, 71, 73, 75, 77, 79, 81, 83, 87, 89, 91, 95, 97, 99, 101, 103, 107, 109, 113, 119, 121, 123, 125, 127

Offset: 1

Author

Naohiro Nomoto, Oct 06 2011

Keywords

• nonn

Comments

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

Programs

Sage

def is_A196736(n): # inefficient, for reference purposes
    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)
# D. S. McNeil, Oct 14 2011