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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

"3-almost prime numbers" are a generalization of primes and semiprimes. As explained in Weisstein: "The primes correspond to the "1-almost prime" numbers 2, 3, 5, 7, 11, ... (A000040). The 2-almost prime numbers correspond to semiprimes 4, 6, 9, 10, 14, 15, 21, 22, ... (A001358). The first few 3-almost 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 4-almost primes are 16, 24, 36, 40, 54, 56, 60, 81, 84, 88, 90, 100, ... (A014613). The first few 5-almost 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

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Last modified October 17 14:28 EDT 2019. Contains 328114 sequences. (Running on oeis4.)