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).

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

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 * A357706 A119123 A293625

Adjacent sequences: A029824 A029825 A029826 * A029828 A029829 A029830

Keyword

nonn

Author

Labos Elemer

Extensions

a(40) corrected by Sean A. Irvine, Mar 05 2020

Status

approved