A143703 a(n) = A143702(n)/2.

1, 3, 7, 15, 15, 21, 15, 39, 91, 555, 285, 915, 3333, 1155, 1267, 2769, 4935, 10005, 70635, 7035, 240045, 77745, 167055, 897429, 1231635, 1066065, 1174695

Offset: 1

Author

Artur Jasinski, Nov 10 2008

Keywords

• nonn
• more

Comments

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

Crossrefs

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

Programs

Mathematica

aa = {1}; bb = {1}; rr = {1}; 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, r]; AppendTo[a, {x, logmax}], {x, 2, 15}]; rr (* Artur Jasinski with assistance of M. F. Hasler *)

Extensions

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