Sequence of distinct least positive numbers such that the average of the first n terms is a cube.

Terms

a(0) =1a(1) =15a(2) =8a(3) =84a(4) =27a(5) =249a(6) =64a(7) =552a(8) =125a(9) =1035a(10) =216a(11) =1740a(12) =343a(13) =2709a(14) =512a(15) =3984a(16) =729a(17) =5607a(18) =1000a(19) =7620a(20) =1331a(21) =10065a(22) =1728a(23) =12984a(24) =2197a(25) =16419a(26) =2744a(27) =20412a(28) =3375a(29) =25005