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 A113941 Pentagonal numbers (A000326) that are also brilliant numbers (A078972). 2
 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; text; internal format)
 OFFSET 1,1 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, Apr 05 2009 LINKS Table of n, a(n) for n=1..32. FORMULA A000326 INTERSECTION A078972. 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, Apr 05 2009 17767 is the 109th pentagonal number and 17767=109*163 is brilliant. CROSSREFS Cf. A000326, A078972, A159190. Cf. A001222, A001248, A001358, A113940, A114439. Sequence in context: A220208 A068722 A255584 * A067238 A372927 A267022 Adjacent sequences: A113938 A113939 A113940 * A113942 A113943 A113944 KEYWORD base,nonn AUTHOR Giovanni Resta, Jan 31 2006 EXTENSIONS Edited by N. J. A. Sloane, Apr 07 2009 at the suggestion of R. J. Mathar Two more terms from R. J. Mathar, Apr 06 2009 STATUS approved

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Last modified August 15 13:43 EDT 2024. Contains 375173 sequences. (Running on oeis4.)