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Search: id:A101605
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| A101605 |
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a(n) = 1 iff n is a product of exactly 3 primes, otherwise 0. |
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19
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| 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)
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OFFSET
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0,1
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COMMENT
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"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.
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LINKS
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Index entries for characteristic functions
Eric Weisstein's World of Mathematics, Almost Prime.
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FORMULA
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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.
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EXAMPLE
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a(28) = 1 because 28 = 2 * 2 * 7 is the product of exactly 3 primes, counted with multiplicity.
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CROSSREFS
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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
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Dec 09 2004
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