A051448 Sum of prime divisors of n (with multiplicity) is a square.

1, 4, 14, 20, 24, 27, 39, 46, 55, 66, 94, 98, 140, 152, 155, 158, 168, 171, 183, 186, 189, 200, 203, 225, 240, 255, 256, 270, 272, 288, 290, 291, 295, 299, 306, 323, 324, 334, 344, 348, 354, 363, 387, 446, 455, 506, 539, 546, 578, 579, 583, 615, 650, 656, 695

Offset: 1

Author

Joe K. Crump (joecr(AT)carolina.rr.com)

Keywords

• easy
• nonn

Comments

Numbers k such that A001414(k) is a perfect square. - Michel Lagneau, May 28 2012

Examples

			a(2) = 14 because 14 = 2*7 and 2 + 7 = 3^2.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Programs

Maple

A:= proc(n) local e, j; e := ifactors(n)[2]: add (e[j][1]*e[j][2], j=1..nops(e)) end:
for m from 1 to 1000 do: m2:=sqrt(A(m)):if m2=floor(m2) then printf(`%d, `, m):else fi:od: # Michel Lagneau, May 28 2012
# second Maple program:
q:= n-> issqr(add(i[1]*i[2], i=ifactors(n)[2])):
select(q, [$1..1000])[];  # Alois P. Heinz, Jan 24 2021

Mathematica

lst = {}; Do[ww = Transpose[FactorInteger[k]]; w = ww[[1]].ww[[2]]; If[IntegerQ[Sqrt[w]], AppendTo[lst, k]], {k, 1, 1000}]; lst (* Michel Lagneau, May 28 2012 *)
Select[Range[700],IntegerQ[Sqrt[Total[Flatten[Table[#[[1]],#[[2]]]&/@ FactorInteger[ #]]]]]&] (* Harvey P. Dale, Dec 12 2018 *)

Extensions

More terms from James Sellers, Sep 08 2000