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Search: id:A144581
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| A144581 |
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Triangular numbers k*(k+1)/2 such that (number of prime factors of k) + (number of prime factors of k+1) is composite. |
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+0
2
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| 28, 45, 66, 78, 105, 120, 153, 171, 190, 231, 300, 325, 378, 406, 435, 465, 496, 561, 595, 630, 741, 780, 861, 903, 946, 990, 1128, 1378, 1485, 1540, 1596, 1653, 2016, 2080, 2211, 2278, 2485, 2556, 2628, 2850, 3081, 3160, 3240, 3321, 3570, 3655, 3741
(list; graph; listen)
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OFFSET
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1,1
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EXAMPLE
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7 has one prime factor and 8 = 2*2*2 has three prime factors; 1+3 = 4 is composite, hence 7*8/2 = 28 is in the sequence.
15 = 3*5 has two prime factors and 16=2*2*2*2 has four prime factors; 2+4 = 6 is composite, hence 15*16/2 = 120 is in the sequence.
18 = 2*3*3 has three prime factors and 19 has one prime factors; 3+1 = 4 is composite, hence 18*19/2 = 171 is in the sequence.
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PROGRAM
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(MAGMA) [ k*(k+1)/2: k in [2..86] | not IsPrime(s) where s is &+[ f[2]: f in Factorization(k) ] + &+[ f[2]: f in Factorization(k+1) ] ];
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CROSSREFS
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Cf. A000217 (triangular numbers), A002808 (composite numbers).
See A144552 for another version.
Sequence in context: A025359 A056031 A061826 this_sequence A075875 A116541 A116565
Adjacent sequences: A144578 A144579 A144580 this_sequence A144582 A144583 A144584
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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), Dec 31 2008
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EXTENSIONS
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Edited and corrected by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jan 03 2009
Edited by N. J. A. Sloane (njas(AT)research.att.com), Jan 08 2009
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