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A101605 a(n) = 1 iff n is a product of exactly 3 primes, otherwise 0. +0
19
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; listen)
OFFSET

0,1

COMMENT

"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

Index entries for characteristic functions

Eric Weisstein's World of Mathematics, Almost Prime.

FORMULA

a(n) = 1 iff n has exactly three prime factors (not necessarily distinct), else a(n) = 0. a(n) = 1 iff n is an element of A014612, else a(n) = 0.

EXAMPLE

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

CROSSREFS

Cf. A014612, A101606, A001358, A014613, A014614.

Sequence in context: A037823 A115790 A025460 this_sequence A135133 A011712 A011715

Adjacent sequences: A101602 A101603 A101604 this_sequence A101606 A101607 A101608

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post (jvospost3(AT)gmail.com), Dec 09 2004

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Last modified November 25 20:09 EST 2009. Contains 167514 sequences.


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