A289838 a(n) = A289815(n) * A289816(n).

1, 2, 2, 3, 6, 6, 3, 6, 6, 4, 10, 10, 12, 30, 30, 12, 30, 30, 4, 10, 10, 12, 30, 30, 12, 30, 30, 5, 14, 14, 15, 42, 42, 15, 42, 42, 20, 70, 70, 60, 210, 210, 60, 210, 210, 20, 70, 70, 60, 210, 210, 60, 210, 210, 5, 14, 14, 15, 42, 42, 15, 42, 42, 20, 70, 70

Offset: 0

Author

Rémy Sigrist, Jul 13 2017

Keywords

• nonn
• base
• look

Comments

Each number k > 0 appears 2^omega(k) times (where omega = A001221).

a(A004488(n)) = a(n) for any n >= 0.

The number of distinct prime factors of a(n) equals the number of nonzero digits in the ternary representation of n.

Examples

			a(42) = A289815(42) * A289816(42) = 20 * 3 = 60.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A001221, A004488, A289815, A289816.

Programs

PARI

a(n) = { my (v=1);
       for (o=2, oo,
           if (n==0, return (v));
           if (gcd(v, o)==1 && omega(o)==1,
               if (n % 3, v *= o);
               n \= 3;
           );
       );}

Python

from sympy import gcd, primefactors
def omega(n): return 0 if n==1 else len(primefactors(n))
def a(n):
    v, o = 1, 2
    while True:
        if n==0: return v
        if gcd(v, o)==1 and omega(o)==1:
            if n%3: v*=o
            n //= 3
        o+=1
print([a(n) for n in range(101)]) # Indranil Ghosh, Aug 02 2017