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Sum of prime divisors of n (with multiplicity) is a square.
4

%I #18 Jan 24 2021 10:30:23

%S 1,4,14,20,24,27,39,46,55,66,94,98,140,152,155,158,168,171,183,186,

%T 189,200,203,225,240,255,256,270,272,288,290,291,295,299,306,323,324,

%U 334,344,348,354,363,387,446,455,506,539,546,578,579,583,615,650,656,695

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

%C Numbers k such that A001414(k) is a perfect square. - _Michel Lagneau_, May 28 2012

%H Harvey P. Dale, <a href="/A051448/b051448.txt">Table of n, a(n) for n = 1..1000</a>

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

%p A:= proc(n) local e, j; e := ifactors(n)[2]: add (e[j][1]*e[j][2], j=1..nops(e)) end:

%p 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

%p # second Maple program:

%p q:= n-> issqr(add(i[1]*i[2], i=ifactors(n)[2])):

%p select(q, [$1..1000])[]; # _Alois P. Heinz_, Jan 24 2021

%t 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 *)

%t Select[Range[700],IntegerQ[Sqrt[Total[Flatten[Table[#[[1]],#[[2]]]&/@ FactorInteger[ #]]]]]&] (* _Harvey P. Dale_, Dec 12 2018 *)

%K easy,nonn

%O 1,2

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

%E More terms from _James A. Sellers_, Sep 08 2000