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A320885
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7-smooth but not 5-smooth numbers of the form (ab+1)(ac+1), a > b > c > 0.
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2
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28, 126, 175, 280, 336, 378, 441, 560, 630, 672, 1225, 1470, 1680, 1701, 1792, 2016, 2520, 2835, 3136, 3969, 4200, 5250, 5600, 6860, 7840, 7875, 8400, 8960, 9072, 9408, 11025, 11340, 12096, 13125, 15120, 17640, 19845, 20160, 21000, 23520, 24696, 27440, 30625, 32928, 35000
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OFFSET
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1,1
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COMMENTS
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Corvaja & Zannier show that there are only finitely many p-smooth terms in A180045, for any prime p. This sequences lists these terms for p = 7 without those for p = 5 (A320884), and is therefore finite.
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LINKS
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FORMULA
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MATHEMATICA
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Reap[For[k = 7, k <= 35000, k = k+7, If[FactorInteger[k][[-1, 1]] == 7, If[ Reduce[k == (a b + 1)(a c + 1) && a > b > c > 0, {a, b, c}, Integers] =!= False, Print[k]; Sow[k]]]]][[2, 1]] (* Jean-François Alcover, Dec 07 2018 *)
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PROG
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A320885=select( is_A180045, A080194_list(1e20)) \\ Only initial terms, not the complete sequence. For more efficiency, use is_A180045 or a dedicated implementation inside the nested loops in A080194_list().
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CROSSREFS
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Cf. A080194 (greatest prime factor = 7).
Cf. A180045 (numbers (ab+1)(ac+1), a>b>c>0), A320883 (subsequence of 3-smooth terms), A320884 (subsequence of 5-smooth terms).
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KEYWORD
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nonn,fini
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AUTHOR
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STATUS
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approved
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