A384498 Squarefree numbers whose distinct prime factors can be partitioned into two sets with equal sums.

1, 30, 70, 286, 646, 1798, 2145, 2310, 2730, 3135, 3526, 3570, 4641, 4845, 5005, 5610, 6006, 6279, 6630, 7198, 7410, 7854, 8778, 8855, 8970, 9177, 10366, 10374, 10626, 10695, 11305, 11571, 11730, 13110, 13485, 13566, 13585, 15470, 16095, 16302, 16422, 16530

Offset: 1

Author

Alois P. Heinz, May 31 2025

Keywords

• nonn

Examples

			2145 = 3*5*11*13 is a term because it is squarefree and 3+13 = 5+11.
16422 = 2*3*7*17*23 is squarefree and 2+7+17 = 3+23.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A005117 and A221054.

Cf. A071141, A071142, A071312.

Programs

Maple

q:= n-> (l-> {l[.., 2][]} minus {1}={} and (s->
        (m-> m::even and coeff(mul(1+x^j, j=s), x, m/2)>0)
        (add(i, i=s)))({l[.., 1][]}))(ifactors(n)[2]):
select(q, [$1..20000])[];

Mathematica

Join[{1},Select[Range[16600],SquareFreeQ[#]&&MemberQ[Total/@Subsets[First/@FactorInteger[#]],Total[First/@FactorInteger[#]]/2]&]] (* James C. McMahon, Jun 02 2025 *)