A185166 Number of prime divisors of n (counted with multiplicity) of numbers k such that sum of proper divisors of k exceeds that of all smaller numbers.

0, 1, 2, 2, 3, 2, 3, 3, 3, 4, 3, 4, 5, 4, 5, 4, 4, 6, 5, 5, 6, 5, 5, 6, 6, 7, 5, 6, 6, 5, 7, 6, 6, 6, 5, 7, 6, 8, 7, 7, 7, 6, 8, 6, 7, 6, 6, 8, 6, 8, 7, 9, 7, 8, 8, 8, 7, 7, 7, 9, 6, 7, 8, 7, 7, 7, 9, 9, 8, 8, 7, 9, 7, 8, 8, 8, 7, 9, 7, 9, 8, 8, 10, 8, 9, 9, 9

Offset: 1

Author

Jonathan Vos Post, Feb 19 2011

Keywords

• nonn

Examples

			a(1) = 0 because 1 = A034090(1) has no prime factors.
a(2) = 1 because 2 = A034090(2) has one prime factor, itself.
a(3) = 2 because 4 = A034090(3) = 2^2 has two prime factors (with multiplicity).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000 (calculated from the b-file at A034090)

Crossrefs

Cf. A001222, A034090, A001065, A034091, A034287, A034288.

Formula

a(n) = A001222(A034090(n)).

Extensions

More terms from Amiram Eldar, Aug 30 2019