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A113941
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Pentagonal numbers (A000326) that are also brilliant numbers (A078972).
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1
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35, 247, 1247, 2501, 4187, 15251, 17767, 33227, 49051, 63551, 68587, 71177, 76501, 81317, 96647, 112477, 118301, 128627, 147737, 159251, 182527, 241001, 250717, 265651, 302177, 318551, 438751, 485357, 563347, 655051, 1563151, 1600117
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| This is to pentagonal numbers A000326 as A113940 is to triangular numbers A000217. These may be seen as the 5th and 3rd row of an infinite array of k-gonal numbers which are also brilliant numbers, where the 4th row is A001248 squares of primes. - Jonathan Vos Post (jvospost3(AT)gmail.com), Apr 05 2009
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FORMULA
| A000326 INTERSECTION A078972.
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EXAMPLE
| a(1) = 35 = 5th pentagonal number = 5*(3*5-1)/2 = 5 * 7, with the two prime factors each being one digit in length. a(2) = 247 = 13th pentagonal number = 13*(3*13-1)/2 = 13 * 19, with the two prime factors each being two digits in length. a(6) = 15251 = 101 * 151, with the two prime factors each being three digits in length. - Jonathan Vos Post (jvospost3(AT)gmail.com), Apr 05 2009
17767 is the 109-th pentagonal number and 17767=109*163 is brilliant.
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CROSSREFS
| Cf. A000326, A078972, A159190.
Cf. A001222, A001248, A001358, A113940, A114439.
Sequence in context: A104474 A171471 A068722 * A067238 A145014 A090646
Adjacent sequences: A113938 A113939 A113940 * A113942 A113943 A113944
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KEYWORD
| base,nonn
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AUTHOR
| Giovanni Resta (g.resta(AT)iit.cnr.it), Jan 31 2006
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EXTENSIONS
| Edited by N. J. A. Sloane, Apr 07 2009 at the suggestion of R. J. Mathar
Two more terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 06 2009
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