A289712 Smallest integer such that the sum of its n smallest divisors is a square.

1, 3, 15, 22, 12, 36, 24, 66, 126, 420, 90, 364, 270, 264, 240, 210, 672, 780, 864, 1050, 672, 720, 924, 1092, 1344, 3240, 3312, 1260, 3600, 1200, 8910, 1080, 27104, 5940, 1680, 8568, 8910, 14280, 6384, 5670, 5544, 9600, 43092, 42900, 5280, 3360, 9504, 8580, 21600, 54288

Offset: 1

Author

Michel Lagneau, Sep 02 2017

Keywords

• nonn

Comments

The first corresponding squares are 1, 4, 9, 36, 16, 25, 36, 144, 81, ...

The first squares in the sequence are 1, 36, 3600, ...

Examples

			a(4)=22 because the sum of the first 4 divisors of 22, i.e., 1 + 2 + 11 + 22 = 36, is a square, and 22 is the smallest integer with this property.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..241

Crossrefs

Cf. A000290, A027750, A240698, A289776.

Programs

Maple

N:= 5*10^5: # to get terms before the first term > N
for k from 1 to N do
  d:= sort(convert(numtheory:-divisors(k),list));
  s:= ListTools:-PartialSums(d);
  for m from 1 to nops(d) do
    if not assigned(A[m]) and issqr(s[m]) then A[m]:= k fi
  od
od:
iA:= map(op,{indices(A)}):
seq(A[i],i=1..min({$1..max(iA)+1} minus iA)-1); # Robert Israel, Oct 01 2017

Mathematica

Table[k=1;While[Nand[Length@#>=n,IntegerQ[Sqrt[Total@Take[PadRight[#,n],n]]]]&@Divisors@k,k++];k,{n,1,50}] (* Program from Michael De Vlieger adapted for this sequence. See A289776. *)

PARI

isok(k, n) = {my(v = divisors(k)); if (#v < n, return(0)); issquare(sum(j=1, n, v[j]));}
a(n) = {my(k = 1); while(!isok(k,n), k++); k;} \\ Michel Marcus, Sep 04 2017