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 A303332 7-smooth numbers representable as the sum of two relatively prime 7-smooth numbers. 0
 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 21, 25, 27, 28, 32, 35, 36, 49, 50, 54, 64, 81, 125, 126, 128, 135, 189, 225, 245, 250, 256, 343, 375, 625, 1029, 2401, 4375 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS It follows from Theorem 6.3 of de Weger's tract that there are exactly 40 terms, the largest of which is 4375 = 1 + 4374 = 5^4 * 7 = 1 + 2 * 3^7. Indeed, de Weger determined all solutions of the equation x + y = z with x, y, z 13-smooth, x, y relatively prime and x <= y; there exist exactly 545 solutions. Among them, exactly 63 solutions consist of 7-smooth numbers, which yields exactly 40 terms of this sequence. REFERENCES T. N. Shorey and R. Tijdeman, Exponential Diophantine Equations, Cambridge University Press, 1986. LINKS B. M. M. de Weger, Algorithms for Diophantine Equations, Centrum voor Wiskunde en Informatica, Amsterdam, 1989. EXAMPLE a(13) = 16 = 1 + 15 = 7 + 9 = 2^4 = 1 + 3 * 5 = 7 + 3^2. a(25) = 81 = 1 + 80 = 25 + 56 = 32 + 49 = 3^4 = 1 + 2^4 * 5 = 5^2 + 2^3 * 7 = 2^5 + 7^2. MATHEMATICA s7 = Select[Range, FactorInteger[#][[-1, 1]] <= 7 &]; Select[s7, AnyTrue[ IntegerPartitions[#, {2}, s7], GCD @@ # == 1 &] &] (* Giovanni Resta, May 30 2018 *) CROSSREFS Cf. A085153 (subsequence) Sequence in context: A096503 A055238 A100952 * A030477 A178859 A165412 Adjacent sequences:  A303329 A303330 A303331 * A303333 A303334 A303335 KEYWORD nonn,fini,full AUTHOR Tomohiro Yamada, May 29 2018 STATUS approved

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Last modified August 14 13:34 EDT 2020. Contains 336480 sequences. (Running on oeis4.)