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A334655 Number of integers less than n with the same number of distinct prime factors as n. 3
0, 0, 1, 2, 3, 0, 4, 5, 6, 1, 7, 2, 8, 3, 4, 9, 10, 5, 11, 6, 7, 8, 12, 9, 13, 10, 14, 11, 15, 0, 16, 17, 12, 13, 14, 15, 18, 16, 17, 18, 19, 1, 20, 19, 20, 21, 21, 22, 22, 23, 24, 25, 23, 26, 27, 28, 29, 30, 24, 2, 25, 31, 32, 26, 33, 3, 27, 34, 35, 4, 28, 36, 29, 37, 38, 39, 40, 5, 30, 41 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Table of n, a(n) for n=1..80.

FORMULA

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

a(n) = A067003(n) - 1.

EXAMPLE

a(12) = 2 because omega(12) = 2 and also omega(6) = omega(10) = 2.

MATHEMATICA

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

PROG

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

CROSSREFS

Cf. A001221, A002110 (positions of 0's), A047983, A067003, A067004, A322837, A322841, A335097.

Sequence in context: A193331 A091246 A271439 * A343410 A133637 A258093

Adjacent sequences:  A334652 A334653 A334654 * A334656 A334657 A334658

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Oct 31 2020

STATUS

approved

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Last modified November 30 06:28 EST 2021. Contains 349419 sequences. (Running on oeis4.)