A328562 Unitary weird numbers (A064114) that are not weird numbers (A006037).

5390, 11830, 17010, 20230, 25270, 37030, 51030, 58870, 67270, 93170, 95830, 117670, 129430, 153090, 153790, 154630, 196630, 243670, 260470, 314230, 343910, 352870, 373030, 436870, 459270, 480130, 482230, 554470, 658630, 714070, 742630, 801430, 831670, 851690, 893830

Offset: 1

Author

Amiram Eldar, Oct 19 2019

Keywords

• nonn

Comments

All the terms are nonsquarefree, since unitary weird numbers that are squarefree are necessarily also weird.

Nonsquarefree unitary weird numbers that are also weird numbers are listed in A328563.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005117, A006037, A013929, A064114, A292705, A328563.

Programs

Mathematica

weirdQ[n_, d_, s1_, m1_] := weirdQ[n, d, s1, m1] = Module[{s = s1, m = m1}, If[m == 0, False, While[d[[m]] > n, s -= d[[m]]; m--]; d[[m]] < n && If[s > n, weirdQ[n - d[[m]], d, s - d[[m]], m - 1] && weirdQ[n, d, s - d[[m]], m - 1], s < n && m < Length[d] - 1]]];
wQ[n_] := Module[{d = Divisors[n]}, s = Total@d - n; m = Length[d] - 1; weirdQ[n, d, s, m]];
uQ[n_] := Module[{d = Select[Divisors[n], GCD[#, n/#] == 1 &]}, s = Total@d - n; m = Length[d] - 1; weirdQ[n, d, s, m]];
aQ[n_] := uQ[n] && ! wQ[n]; Select[Range[10^6], aQ]
(* after M. F. Hasler's pari code at A006037 *)