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A030059
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Numbers that are the product of an odd number of distinct primes.
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8
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2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 30, 31, 37, 41, 42, 43, 47, 53, 59, 61, 66, 67, 70, 71, 73, 78, 79, 83, 89, 97, 101, 102, 103, 105, 107, 109, 110, 113, 114, 127, 130, 131, 137, 138, 139, 149, 151, 154, 157, 163, 165, 167, 170, 173, 174, 179, 181, 182, 186, 190, 191, 193
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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REFERENCES
| Ramanujan, Collected Papers, pp. xxiv, 21.
B. C. Berndt & R. A. Rankin, Ramanujan: Letters and Commentary, see p. 23; AMS Providence RI 1995.
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
S. Ramanujan, Irregular numbers, J. Indian Math. Soc. 5 (1913) 105-106.
Eric Weisstein's World of Mathematics, Prime Factor
Eric Weisstein's World of Mathematics, Moebius Function
Eric Weisstein's World of Mathematics, Prime Sums
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FORMULA
| omega(a(n)) = A001221(a(n)) gives A005408. {primes A000040} UNION {sphenic numbers A007304} UNION {numbers that are divisible by exactly 5 different primes A051270} UNION {products of 7 distinct primes (squarefree 7-almost primes) A123321} UNION {products of 9 distinct primes; also n has exactly 9 distinct prime factors and n is squarefree A115343} UNION.... - Jonathan Vos Post (jvospost3(AT)gmail.com), Oct 19 2007
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MAPLE
| a := n -> `if`(numtheory[mobius](n)=-1, n, NULL); seq(a(i), i=1..193); [From Peter Luschny (peter(AT)luschny.de), May 04 2009]
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CROSSREFS
| Cf. A000040, A001221, A005408, A007304, A030231, A051270, A123321.
Sequence in context: A197300 A095959 A028905 * A201879 A089063 A171019
Adjacent sequences: A030056 A030057 A030058 * A030060 A030061 A030062
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from David W. Wilson (davidwwilson(AT)comcast.net)
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