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

1,2

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, ...

Links

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

Example

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.

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. *)

Prog

(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

Crossrefs

Cf. A000290, A027750, A240698, A289776.

Sequence in context: A212846 A276804 A009057 * A083795 A083793 A324127

Adjacent sequences: A289709 A289710 A289711 * A289713 A289714 A289715

Keyword

nonn

Author

Michel Lagneau, Sep 02 2017

Status

approved