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

1,12

Links

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

Formula

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

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

Example

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.

Mathematica

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

Prog

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

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.

Sequence in context: A051659 A085861 A326197 * A376847 A261812 A077266

Adjacent sequences: A325223 A325224 A325225 * A325227 A325228 A325229

Keyword

nonn

Author

Gus Wiseman, Apr 12 2019

Extensions

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

Status

approved