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A335097 Number of integers less than n with the same number of prime factors (counted with multiplicity) as n. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = |{j < n : bigomega(j) = bigomega(n)}|.

a(n) = A058933(n) - 1.

EXAMPLE

a(10) = 3 because bigomega(10) = 2 and also bigomega(4) = bigomega(6) = bigomega(9) = 2.

MAPLE

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

MATHEMATICA

Table[Length[Select[Range[n - 1], PrimeOmega[#] == PrimeOmega[n] &]], {n, 80}]

PROG

(PARI) a(n)={my(t=bigomega(n)); sum(k=1, n-1, bigomega(k)==t)} \\ Andrew Howroyd, Oct 31 2020

CROSSREFS

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

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Oct 31 2020

STATUS

approved

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Last modified May 19 17:44 EDT 2022. Contains 353847 sequences. (Running on oeis4.)