A115355 a(n) is the smallest number representable in exactly n ways as a sum of 3 powerful(1) numbers.

3, 17, 33, 41, 66, 77, 89, 117, 133, 145, 153, 189, 161, 225, 301, 257, 324, 333, 341, 297, 432, 425, 369, 517, 613, 441, 521, 585, 513, 809, 689, 792, 657, 1001, 801, 881, 1000, 1017, 873, 945, 900, 1265, 1169, 1425, 1089, 1125, 1197, 1481, 1161, 1584

Offset: 1

Author

Giovanni Resta, Jan 21 2006

Keywords

• nonn

Comments

Here we are considering powerful numbers (first definition) A001694. Note that, by definition, 1 is powerful.

Examples

			a(2) = 17 since 17 = 4+4+9 = 8+8+1.
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Powerful Number.

Crossrefs

Cf. A001694, A085252, A085253, A085254, A085255, A063274, A115354.

Programs

Mathematica

pwfQ[n_] := n==1 || Min[Transpose[FactorInteger@n][[2]]] > 1; lim = 5000; pt = Select[Range[lim], pwfQ]; t = Table[0, {i, lim}]; Do[v = pt[[i]]+pt[[j]]+pt[[k]]; If[v <= lim, t[[v]]++ ], {i, Length@pt}, {j, i}, {k, j}]; Table[Position[t, k][[1, 1]], {k, 60}]