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A325226 Number of prime factors of n that are less than the largest, counted with multiplicity. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,12
LINKS
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.
Sequence in context: A051659 A085861 A326197 * A261812 A077266 A366794
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

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Last modified March 29 09:32 EDT 2024. Contains 371268 sequences. (Running on oeis4.)