

A101605


a(n) = 1 if n is a product of exactly 3 (not necessarily distinct) primes, otherwise 0.


22



0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0
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OFFSET

1,1


COMMENTS

"3almost prime numbers" are a generalization of primes and semiprimes. As explained in Weisstein: "The primes correspond to the "1almost prime" numbers 2, 3, 5, 7, 11, ... (A000040). The 2almost prime numbers correspond to semiprimes 4, 6, 9, 10, 14, 15, 21, 22, ... (A001358). The first few 3almost primes are 8, 12, 18, 20, 27, 28, 30, 42, 44, 45, 50, 52, 63, 66, 68, 70, 75, 76, 78, 92, 98, 99, ... (A014612). The first few 4almost primes are 16, 24, 36, 40, 54, 56, 60, 81, 84, 88, 90, 100, ... (A014613). The first few 5almost primes are 32, 48, 72, 80, ... (A014614)." See A101606 for the Inverse Moebius Transform of this sequence.


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Almost Prime.
Index entries for characteristic functions
Index entries for sequences computed from exponents in factorization of n


FORMULA

a(n) = 1 if n has exactly three prime factors (not necessarily distinct), else a(n) = 0. a(n) = 1 if n is an element of A014612, else a(n) = 0.
a(n) = floor(Omega(n)/3) * floor(3/Omega(n)).  Wesley Ivan Hurt, Jan 10 2013


EXAMPLE

a(28) = 1 because 28 = 2 * 2 * 7 is the product of exactly 3 primes, counted with multiplicity.


MAPLE

A101605 := proc(n)
if numtheory[bigomega](n) = 3 then
1;
else
0;
end if;
end proc: # R. J. Mathar, Mar 13 2015


PROG

(PARI) is(n)=bigomega(n)==3 \\ Charles R Greathouse IV, Apr 25 2016


CROSSREFS

Cf. A000040, A001358, A014612, A014613, A014614, A101606, A123074.
Sequence in context: A115790 A025460 A169673 * A175854 A135133 A011712
Adjacent sequences: A101602 A101603 A101604 * A101606 A101607 A101608


KEYWORD

easy,nonn


AUTHOR

Jonathan Vos Post, Dec 09 2004


EXTENSIONS

Description clarified by Antti Karttunen, Jul 23 2017


STATUS

approved



