A325226 Number of prime factors of n that are less than the largest, counted with multiplicity.

0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 1, 1, 0, 0, 1, 0, 2, 1, 1, 0, 3, 0, 1, 0, 2, 0, 2, 0, 0, 1, 1, 1, 2, 0, 1, 1, 3, 0, 2, 0, 2, 2, 1, 0, 4, 0, 1, 1, 2, 0, 1, 1, 3, 1, 1, 0, 3, 0, 1, 2, 0, 1, 2, 0, 2, 1, 2, 0, 3, 0, 1, 1, 2, 1, 2, 0, 4, 0, 1, 0, 3, 1, 1, 1, 3, 0, 3, 1, 2, 1, 1, 1, 5, 0, 1, 2, 2, 0, 2, 0, 3, 2

Offset: 1

Author

Gus Wiseman, Apr 12 2019

Keywords

• nonn

Examples

			The prime factors of 300 are {2,2,3,5,5} of which {2,2,3} are less than the largest, so a(300) = 3.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..100000

Crossrefs

Positions of 0's are A000961. Positions of 1's are A325230. Positions of terms > 1 are A307517.

Cf. A000094, A000245, A001222, A052126, A053585, A061395, A062977, A064989, A071178, A105441, A108951, A256617.

Programs

Mathematica

Table[PrimeOmega[n/Power@@FactorInteger[n][[-1]]],{n,100}]

PARI

A071178(n) = if(1==n, 0, factor(n)[omega(n), 2]);
A325226(n) = (bigomega(n) - A071178(n)); \\ Antti Karttunen, Nov 17 2019

Formula

a(n) = A001222(n/A053585(n)).

a(n) = A001222(n) - A071178(n) = A062977(A108951(n)). - Antti Karttunen, Nov 17 2019

Extensions

Data section extended up to term a(105) by Antti Karttunen, Nov 17 2019