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

1,2

Links

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

Example

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.

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 *)

Crossrefs

Intersection of A005117 and A221054.

Cf. A071141, A071142, A071312.

Sequence in context: A131647 A301900 A357854 * A071141 A071312 A071142

Adjacent sequences: A384495 A384496 A384497 * A384499 A384500 A384501

Keyword

nonn

Author

Alois P. Heinz, May 31 2025

Status

approved