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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, 361, 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

Table of n, a(n) for n=1..53.

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

Labos Elemer

STATUS

approved

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Last modified November 14 06:40 EST 2019. Contains 329110 sequences. (Running on oeis4.)