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
KEYWORD
nonn
AUTHOR
Michel Lagneau, Sep 02 2017
STATUS
approved