A360694 -id:A360694 - cp's OEIS frontend

A363967 Numbers whose divisors can be partitioned into two disjoint sets whose both sums are squares.

1, 3, 9, 22, 27, 30, 40, 63, 66, 70, 81, 88, 90, 94, 115, 119, 120, 138, 153, 156, 170, 171, 174, 184, 189, 190, 198, 210, 214, 217, 232, 264, 265, 270, 280, 282, 310, 318, 322, 323, 343, 345, 357, 360, 364, 376, 382, 385, 399, 400, 414, 416, 462, 468, 472, 495, 497

Offset: 1

Amiram Eldar, Jun 30 2023

nonn

If one of the two sets is empty then the term is a number whose sum of divisors is a square (A006532).
If k is a number such that (6*k)^2 is the sum of a twin prime pair (A037073), then (18*k^2)^2 - 1 is a term.
3 is the only prime term.

			9 is a term since its divisors, {1, 3, 9}, can be partitioned into the two disjoint sets, {1, 3} and {9}, whose sums, 1 + 3 = 4 = 2^2 and 9 = 3^2, are both squares.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A000203, A000290, A037073.
Subsequence of A333911.
A006532 is a subsequence.
Similar sequences: A333677, A360694.

sqQ[n_] := IntegerQ[Sqrt[n]]; q[n_] := Module[{d = Divisors[n], s, p}, s = Total[d]; p = Position[Rest @ CoefficientList[Product[1 + x^i, {i, d}], x], _?(# > 0 &)] // Flatten; AnyTrue[p, sqQ[#] && sqQ[s - #] &]]; Select[Range[500], q]

cp's OEIS Frontend

A363967 Numbers whose divisors can be partitioned into two disjoint sets whose both sums are squares.

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