A115354 a(n) is the smallest number representable in exactly n ways as a sum of 2 powerful(1) numbers.

2, 17, 108, 153, 297, 657, 1764, 2052, 4644, 6156, 10800, 16200, 22932, 29000, 11025, 54225, 92025, 68796, 100548, 99225, 44100, 88200, 264600, 431244, 176400, 441000, 666468, 1151172, 352800, 617400, 396900, 926100, 980100, 793800, 1234800

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 = 16+1 = 8+9.
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..120
• Eric Weisstein's World of Mathematics, Powerful Number.

Crossrefs

Cf. A001694, A085252, A085253, A085254, A085255, A063274, A115355.

Programs

Mathematica

pwfQ[n_] := n == 1 || Min[Transpose[FactorInteger@n][[2]]] > 1; lim=200000; pt = Select[Range[lim], pwfQ]; t = Table[0, {i, lim}]; Do[v = pt[[i]]+ pt[[j]]; If[v<=lim, t[[v]]++ ], {i, Length@pt}, {j, i}]; Table[Position[t, k][[1, 1]], {k, 22}]

Extensions

a(23)-a(35) from Donovan Johnson, Dec 07 2008