A188833 -id:A188833 - cp's OEIS frontend

4, 9, 25, 49, 121, 169, 289, 361, 625, 841, 961, 1369, 1681, 1849, 3721, 4489, 5041, 5329, 7921, 9409, 10201, 10609, 11881, 12769, 16129, 17161, 18769, 19321, 22201, 22801, 24649, 32761, 36481, 37249, 38809, 39601, 44521, 52441, 57121, 58081, 63001, 73441

Offset: 1

Vladimir Shevelev, Apr 12 2011

nonn

The sequence contains many squares of primes.
Question 1: What is the sequence of primes whose squares are not in this sequence?  It begins: 23, 47, 53, 59, 79, 83, 107, ... A188833
Question 2: What is the sequence of composite numbers whose squares are in this sequence?  It begins: 25, 289, 361, 529, ...

Cf. A188550, A188579, A188794, A188833.

with(numtheory):
b:= proc(n) local h, i, k, m;
       m, i:= 0, 0;
       for k from 2 to floor(sqrt(n)) do
          h:= nops(select(x-> irem(x, k)=0,
                  [seq (n-d, d=divisors(n-k) minus{1})]));
          if h>m then m, i:= h, k fi
       od; i
    end:
a:= proc(n) option remember; local k;
      for k from 1+ `if` (n=1, 3, a(n-1))
      while not b(k)^2=k do od; k
    end:
seq(a(n), n=1..15);  # Alois P. Heinz, Apr 13 2011

b[n_] := Module[{h, i = 0, k, m = 0}, For[k = 2, k <= Floor[Sqrt[n]], k++, h = Length[Select[Table[n - d, {d, Rest[Divisors[n - k]]}], Mod[#, k] == 0 &]]; If[h > m, {m, i} = {h, k}]]; i];
Reap[For[n = 1, n <= 80000, n++, If[b[n]^2==n, Print[n]; Sow[n]]]][[2, 1]] (* Jean-François Alcover, Nov 11 2020, after Alois P. Heinz *)

cp's OEIS Frontend

A188836 Numbers n for which A188794(n)^2 = n.

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