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A335097
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Number of integers less than n with the same number of prime factors (counted with multiplicity) as n.
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4
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0, 0, 1, 0, 2, 1, 3, 0, 2, 3, 4, 1, 5, 4, 5, 0, 6, 2, 7, 3, 6, 7, 8, 1, 8, 9, 4, 5, 9, 6, 10, 0, 10, 11, 12, 2, 11, 13, 14, 3, 12, 7, 13, 8, 9, 15, 14, 1, 16, 10, 17, 11, 15, 4, 18, 5, 19, 20, 16, 6, 17, 21, 12, 0, 22, 13, 18, 14, 23, 15, 19, 2, 20, 24, 16, 17, 25, 18, 21, 3
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history;
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OFFSET
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1,5
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LINKS
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Robert Israel, Table of n, a(n) for n = 1..10000
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FORMULA
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a(n) = |{j < n : bigomega(j) = bigomega(n)}|.
a(n) = A058933(n) - 1.
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EXAMPLE
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a(10) = 3 because bigomega(10) = 2 and also bigomega(4) = bigomega(6) = bigomega(9) = 2.
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MAPLE
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A:= NULL:
for n from 1 to 100 do
t:= numtheory:-bigomega(n);
if not assigned(R[t]) then
A:= A, 0;
R[t]:= 1;
else
A:= A, R[t];
R[t]:= R[t]+1;
fi
od:
A; # Robert Israel, Oct 24 2021
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MATHEMATICA
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Table[Length[Select[Range[n - 1], PrimeOmega[#] == PrimeOmega[n] &]], {n, 80}]
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PROG
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(PARI) a(n)={my(t=bigomega(n)); sum(k=1, n-1, bigomega(k)==t)} \\ Andrew Howroyd, Oct 31 2020
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CROSSREFS
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Cf. A000079 (positions of 0's), A001222, A047983, A058933, A067004, A322838, A334655.
Sequence in context: A035157 A318995 A217176 * A334312 A087469 A022328
Adjacent sequences: A335094 A335095 A335096 * A335098 A335099 A335100
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KEYWORD
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nonn
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AUTHOR
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Ilya Gutkovskiy, Oct 31 2020
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STATUS
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approved
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