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A055037
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Number of numbers <= n with an even number of prime factors (counted with multiplicity).
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7
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1, 1, 1, 2, 2, 3, 3, 3, 4, 5, 5, 5, 5, 6, 7, 8, 8, 8, 8, 8, 9, 10, 10, 11, 12, 13, 13, 13, 13, 13, 13, 13, 14, 15, 16, 17, 17, 18, 19, 20, 20, 20, 20, 20, 20, 21, 21, 21, 22, 22, 23, 23, 23, 24, 25, 26, 27, 28, 28, 29, 29, 30, 30, 31, 32, 32, 32, 32, 33, 33, 33, 33, 33, 34, 34, 34
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OFFSET
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1,4
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COMMENTS
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LINKS
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FORMULA
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(1/2)*Sum_{k=1..n} (1+lambda(k)) = (1/2)*(n+L(n)), where lambda(n)=A008836(n) and L(n)=A002819(n).
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MATHEMATICA
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Table[Length[Select[Range[n], EvenQ[PrimeOmega[#]] &]], {n, 75}] (* Alonso del Arte, May 28 2012 *)
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PROG
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(Python)
from functools import reduce
from operator import ixor
from sympy import factorint
def A055037(n): return sum(1 for i in range(1, n+1) if not (reduce(ixor, factorint(i).values(), 0)&1)) # Chai Wah Wu, Jan 01 2023
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Antreas P. Hatzipolakis (xpolakis(AT)otenet.gr), Jun 01 2000
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EXTENSIONS
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STATUS
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approved
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