Numbers k such that A006577(k^2) sets a new record.

Terms

a(0) =2a(1) =3a(2) =5a(3) =7a(4) =10a(5) =11a(6) =22a(7) =35a(8) =45a(9) =49a(10) =51a(11) =77a(12) =123a(13) =143a(14) =269a(15) =419a(16) =429a(17) =765a(18) =1011a(19) =1395a(20) =1989a(21) =2165a(22) =3335a(23) =3827a(24) =7179a(25) =9005a(26) =18010a(27) =36020a(28) =41453a(29) =82906