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 A029827 Composite connected numbers: composite numbers k such that g(k) < g(u) + g(v) holds for all relatively prime factorizations k=u*v, where g(x) = ceiling(log_2 x). 9
 15, 45, 51, 55, 57, 63, 85, 95, 99, 111, 115, 117, 119, 123, 153, 171, 185, 187, 201, 205, 207, 209, 213, 215, 219, 221, 225, 231, 235, 237, 245, 247, 249, 253, 255, 323, 333, 335, 355, 365, 369, 387, 391, 393, 395, 405, 407, 411, 415, 417, 423, 425, 429 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Prime powers are not connected since they have no relatively prime factorizations. - Michel Marcus, Feb 25 2014 REFERENCES E. Labos, Spike Generating Dynamical Systems and Networks, In Lect. Notes in Economics and Mathematical Systems, pp. 189-206. Springer Verlag 1985. LINKS EXAMPLE k = 46665 = 5*9*17*61 is not a connected number because k = 61*765, but 16 >= 6 + 10. PROG (PARI) g(n) = ceil(log(n)/log(2)); isok(n) = {if (isprime(n), return (0)); d = divisors(n); gn = g(n); bpf = 0; for (i=2, #d-1, di = d[i]; if (gcd(di, n/di)==1, bpf = 1; if (gn >= g(di)+g(n/di), return (0)); ); ); return (bpf); } \\ Michel Marcus, Feb 25 2014 CROSSREFS Cf. A029837, A036381-A036390, A034444. Sequence in context: A292018 A289669 A295980 * A119123 A293625 A084821 Adjacent sequences:  A029824 A029825 A029826 * A029828 A029829 A029830 KEYWORD nonn AUTHOR EXTENSIONS a(40) corrected by Sean A. Irvine, Mar 05 2020 STATUS approved

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Last modified October 27 01:02 EDT 2020. Contains 338035 sequences. (Running on oeis4.)