A085255 Numbers having at least two representations as a sum of two powerful numbers (A001694).

17, 33, 36, 40, 41, 50, 52, 57, 65, 68, 72, 73, 76, 80, 81, 85, 89, 97, 104, 108, 109, 113, 116, 117, 125, 129, 130, 132, 133, 136, 137, 144, 145, 148, 152, 153, 157, 160, 164, 170, 172, 177, 180, 185, 189, 193, 197, 200, 201, 204, 205, 208, 209, 216, 221

Offset: 1

Author

Reinhard Zumkeller, Jun 23 2003

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Powerful Number.

Crossrefs

Cf. A001694, A076871, A085252, A085253, A085254.

Programs

Mathematica

With[{m = 222}, pow = Select[Range[m], # == 1 || Min[FactorInteger[#][[;; , 2]]] > 1 &]; Position[BinCounts[Select[Plus @@@ Union[Sort /@ Tuples[pow, {2}]], # <= m &], {1, m, 1}], ?(# > 1 &)] // Flatten] (* _Amiram Eldar, Jan 30 2023 *)

Formula

A085252(a(n)) > 1.