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A327877 Numbers having an odd number of non-unitary prime factors. 1
4, 8, 9, 12, 16, 18, 20, 24, 25, 27, 28, 32, 40, 44, 45, 48, 49, 50, 52, 54, 56, 60, 63, 64, 68, 75, 76, 80, 81, 84, 88, 90, 92, 96, 98, 99, 104, 112, 116, 117, 120, 121, 124, 125, 126, 128, 132, 135, 136, 140, 147, 148, 150, 152, 153, 156, 160, 162, 164, 168 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Differs from A190641(n) from n = 310 (900, the least number with 3 non-unitary prime factors, is in this sequence but not in A190641).

The asymptotic density of the numbers in this sequence is 0.338682... = 1 - A065493.

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

Eckford Cohen, Some asymptotic formulas in the theory of numbers, Transactions of the American Mathematical Society, Vol. 112, No. 2, (1964), pp. 214-227.

Willy Feller and Erhard Tornier, Mengentheoretische Untersuchung von Eigenschaften der Zahlenreihe, Mathematische Annalen, Vol. 107, No. 1 (1933), pp. 188-232.

I. J. Schoenberg, On asymptotic distributions of arithmetical functions, Transactions of the American Mathematical Society, Vol. 39, No. 2 (1936), pp. 315-330.

MATHEMATICA

A056170[n_] := Count[FactorInteger[n], {_, k_ /; k > 1}]; Select[Range[200], OddQ[A056170[#]] &] (* after Jean-Fran├žois Alcover at A056170 *)

PROG

(PARI) \\ here b(n) is A056170(n)

b(n)={my(f=factor(n)[, 2]); sum(i=1, #f, f[i]>1)}

{ select(k->b(k)%2, [1..200]) } \\ Andrew Howroyd, Sep 28 2019

CROSSREFS

Cf. A056170, A065493, A190641.

Sequence in context: A013929 A162966 A190641 * A034043 A278517 A053443

Adjacent sequences:  A327874 A327875 A327876 * A327878 A327879 A327880

KEYWORD

nonn

AUTHOR

Amiram Eldar, Sep 28 2019

STATUS

approved

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Last modified April 5 09:46 EDT 2020. Contains 333239 sequences. (Running on oeis4.)