A085254 Numbers having a unique representation as sum of two powerful numbers (A001694).

2, 5, 8, 9, 10, 12, 13, 16, 18, 20, 24, 25, 26, 28, 29, 31, 32, 34, 35, 37, 43, 44, 45, 48, 53, 54, 58, 59, 61, 63, 64, 74, 82, 88, 90, 91, 96, 98, 99, 100, 101, 106, 112, 121, 122, 124, 126, 127, 128, 134, 135, 140, 141, 146, 149, 150, 155, 161, 162, 169, 171

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, A085255.

Programs

Mathematica

With[{m = 180}, 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.