A292705 -id:A292705 - cp's OEIS frontend

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

Amiram Eldar, Oct 19 2019

nonn

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.

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

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

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 *)

A328563 Nonsquarefree unitary weird numbers that are also weird numbers.

Original entry on oeis.org

1554070, 1596070, 1725430, 1859830, 1952230, 2095030, 2242870, 2293270, 2553670, 2607430, 2716630, 2772070, 3116470, 3481030, 3607030, 3670870, 3800230, 3998470, 4065670, 4410070, 4623430, 4841830, 5065270, 5140870, 5371030, 5527270, 5606230, 6009430, 6597430

Offset: 1

Amiram Eldar, Oct 19 2019

nonn

The nonsquarefree unitary weird numbers that are not weird numbers are listed in A328562.

Amiram Eldar, Table of n, a(n) for n = 1..15716 (terms below 10^10)

Subsequence of A064114.
Intersection of A006037 and A292705.
Cf. A328562.

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]]];
aQ[n_] := ! SquareFreeQ[n] && Module[{d = Divisors[n]}, s = Total@d - n; m = Length[d] - 1; Total@Select[d, GCD[#, n/#] == 1 &] > 2 n && weirdQ[n, d, s, m]]; Select[Range[10^7], aQ]
(* after M. F. Hasler's pari code at A006037 *)

cp's OEIS Frontend

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

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