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A144549
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Triangular numbers p*(p+1)/2 with p prime such that 1+(number of prime factors of p+1) is prime.
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0
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3, 6, 15, 91, 276, 703, 1431, 1770, 1891, 2701, 3486, 4005, 5356, 8646, 9730, 11175, 11476, 12403, 18721, 19503, 24976, 25878, 27261, 28680, 38503, 43071, 47278, 49141, 60378, 61075, 64620, 72010, 75855, 79003, 88831, 98346, 104653, 106491
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Triangular numbers n(n+1)/2 such that n and A073093(n+1) are both prime. Subsequence of A034953. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 03 2009]
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EXAMPLE
| 3 has one prime factor; 1+1 = 2 is prime, hence 2*3/2 = 3 is in the sequence.
14 = 2*7 has two prime factors; 1+2 = 3 is prime, hence 13*14/2 = 91 is in the sequence.
24 = 2*2*2*3 has four prime factors; 1+4 = 5 is prime, hence 23*24/2 = 276 is in the sequence.
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PROG
| (MAGMA) [ p*(p+1)/2: p in PrimesUpTo(490) | IsPrime(1 + &+[ f[2]: f in Factorization(p+1) ]) ];
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CROSSREFS
| Cf. A000217 (triangular numbers), A000040 (prime numbers), A001222 (number of prime divisors of n).
Sequence in context: A013273 A013277 A190187 * A013270 A013276 A110809
Adjacent sequences: A144546 A144547 A144548 * A144550 A144551 A144552
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KEYWORD
| nonn
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AUTHOR
| Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Dec 31 2008
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EXTENSIONS
| Edited, corrected (3 inserted) and extended beyond a(16) by Klaus Brockhaus, Jan 05 2009
3 inserted and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 03 2009
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