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A101637
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a(n) = 1 iff n is a 4-almost prime, else 0.
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15
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| See A101638 for the inverse Moebius transform of this sequence. 4-almost primes are a generalization of primes and semiprimes. Each 4-almost primes is the product of two (not necessarily distinct) 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)."
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LINKS
| Index entries for characteristic functions
Eric Weisstein's World of Mathematics, Almost Prime.
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EXAMPLE
| a(100) = 1 because 100 = 2 * 2 * 5 * 5 is the product of exactly 4 primes and thus is a 4-almost prime.
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CROSSREFS
| Cf. A101638, A014613, A000040, A001358, A014612, A014614.
Sequence in context: A085980 A023974 A011730 * A011729 A011728 A133010
Adjacent sequences: A101634 A101635 A101636 * A101638 A101639 A101640
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KEYWORD
| easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Dec 10 2004
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