A387461 Cyclic composite numbers that are the sum of two squared positive integers.

65, 85, 145, 185, 221, 265, 365, 377, 445, 481, 485, 493, 533, 545, 565, 629, 685, 697, 745, 785, 793, 865, 901, 949, 965, 985, 1037, 1073, 1105, 1145, 1157, 1165, 1189, 1241, 1261, 1285, 1313, 1345, 1385, 1417, 1465, 1469, 1513, 1517, 1537, 1565, 1585, 1649, 1685

Offset

1,1

Links

Table of n, a(n) for n=1..49.

Example

65 and 85 are elements of A387460 and are sums of two squares in two ways: 65 = 8^2 + 1^2 = 4^2 + 7^2, 85 = 2^2 + 9^2 = 6^2 + 7^2.

Maple

isA387461 := proc(n)
    isA000404(n) and isA387460(n) ;
end proc:
A387461 := proc(n)
    option remember ;
    if n =1 then
        65 ;
    else
        for a from procname(n-1)+1 do
            if isA387461(a) then
                return a;
            end if;
        end do:
    end if;
end proc:
seq(A387461(n), n=1..100) ; # R. J. Mathar, Mar 18 2026

Mathematica

q[n_] := Count[PowersRepresentations[n, 2, 2], _?(First[#] > 0 &)] >  0; Select[Range[1, 2000, 4], CompositeQ[#] && CoprimeQ[#, EulerPhi[#]] && q[#] &] (* Amiram Eldar, Aug 29 2025 *)

Crossrefs

Intersection of A000404 and A387460.

Also subset of A003277 and of A050384.

Sequence in context: A274044 A024409 A131574 * A323272 A322781 A020273

Adjacent sequences: A387458 A387459 A387460 * A387462 A387463 A387464

Keyword

nonn

Author

Joel E. Cohen, Aug 29 2025

Status

approved