A143702 a(n) is the minimal values of A007947((2^n)*m*(2^n-m)).

2, 6, 14, 30, 30, 42, 30, 78, 182, 1110, 570, 1830, 6666, 2310, 2534, 5538, 9870, 20010, 141270, 14070, 480090, 155490, 334110, 1794858, 2463270, 2132130, 2349390

Offset: 1

Author

Artur Jasinski, Nov 10 2008

Keywords

• nonn
• more

Comments

The product of distinct prime divisors of (2^n)*m*(2^n-m) is also called the radical of that number: rad((2^n)*m*(2^n-m)).

For numbers m see A143700.

Crossrefs

Cf. A007947, A085152, A085153, A147298-A147307, A147638-A147643.

Programs

Mathematica

aa = {1}; bb = {1}; rr = {2}; Do[logmax = 0; k = 2^x; w = Floor[(k - 1)/2]; Do[m = FactorInteger[n (k - n)]; rad = 1; Do[rad = rad m[[s]][[1]], {s, 1, Length[m]}]; log = Log[k]/Log[rad]; If[log > logmax, bmin = k - n; amax = n; logmax = log; r = rad], {n, 1, w, 2}]; Print[{x, amax}]; AppendTo[aa, amax]; AppendTo[bb, bmin]; AppendTo[rr, 2*r]; AppendTo[a, {x, logmax}], {x, 2, 15}]; rr (* Artur Jasinski with assistance of M. F. Hasler *)

Extensions

Name changed and a(1) added by Jinyuan Wang, Aug 11 2020