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Search: id:A155087
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| A155087 |
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Primes p such that Omega(c(p)) is composite, where Omega(n) is the number of prime divisors of n counted with multiplicity (A001222) and c(n) is the nth composite number (A002808). |
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| 37, 71, 103, 109, 151, 157, 163, 181, 233, 257, 263, 271, 281, 307, 397, 443, 457, 509, 599, 607, 653, 677, 691, 709, 719, 797, 821, 883, 907, 971, 1033, 1049, 1051, 1063, 1069, 1091, 1093, 1097, 1109, 1181, 1277, 1279, 1327, 1361, 1367, 1399, 1429, 1447, 1453, 1489
(list; graph; listen)
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OFFSET
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1,1
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EXAMPLE
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37 is such a prime as the 37th composite number is 54 and Omega(54) = Omega(2^1*3^3) = 4, which is composite. Likewise 71, as c(71) = 96, and Omega(96) = Omega(2^5*3^1) = 6 which is composite. 113 is not such a prime, as Omega(c(113)) = Omega(148) = Omega(2^2*37^1) =3 which is prime.
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MAPLE
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with(numtheory): composites := remove(isprime, [$2..3000]):
A155087:= select(x -> isprime(x) and not isprime(bigomega(composites[x])), [$2..2000]);
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CROSSREFS
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Cf. A000040, A002808.
Sequence in context: A105462 A119381 A138396 this_sequence A044103 A044484 A158065
Adjacent sequences: A155084 A155085 A155086 this_sequence A155088 A155089 A155090
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KEYWORD
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nonn
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AUTHOR
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Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Jan 20 2009, Jan 28 2009
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EXTENSIONS
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Corrected and edited by D. S. McNeil (d.mcneil(AT)qmul.ac.uk), Mar 19 2009
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