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

1,3

Links

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

Formula

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

Example

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).

Crossrefs

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

Sequence in context: A338292 A359728 A217865 * A276555 A348190 A211100

Adjacent sequences: A185163 A185164 A185165 * A185167 A185168 A185169

Keyword

nonn

Author

Jonathan Vos Post, Feb 19 2011

Extensions

More terms from Amiram Eldar, Aug 30 2019

Status

approved