A327877 Numbers having an odd number of non-unitary prime factors.

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

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-François 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, A333634 (complement).

Sequence in context: A350137 A359470 A190641 * A359468 A034043 A278517

Adjacent sequences: A327874 A327875 A327876 * A327878 A327879 A327880

Keyword

nonn

Author

Amiram Eldar, Sep 28 2019

Status

approved