A386294 Nonsquarefree weak numbers k such that A053669(k) < A006530(k).
20, 28, 40, 44, 45, 50, 52, 56, 63, 68, 75, 76, 80, 84, 88, 92, 98, 99, 104, 112, 116, 117, 124, 126, 132, 135, 136, 140, 147, 148, 152, 153, 156, 160, 164, 168, 171, 172, 175, 176, 184, 188, 189, 198, 204, 207, 208, 212, 220, 224, 228, 232, 234, 236, 242, 244
Offset: 1
Keywords
Examples
Table of n, a(n) and prime decomposition for n = 1..12: n a(n) ------------------ 1 20 = 2^2 * 5 2 28 = 2^2 * 7 3 40 = 2^3 * 5 4 44 = 2^2 * 11 5 45 = 3^2 * 5 6 50 = 2 * 5^2 7 52 = 2^2 * 13 8 56 = 2^3 * 7 9 63 = 3^2 * 7 10 68 = 2^2 * 17 11 75 = 3 * 5^2 12 76 = 2^2 * 19 Let q = A053669 and let gpf = A006530. The number 12 = 2^2*3 is not in the sequence since q(12) > gpf(12), i.e., 5 > 3. The number 18 = 2*3^2 is not in the sequence since q(18) > gpf(18), i.e., 5 > 3. a(1) = 20 = 2^2*5 since q(20) < gpf(20), i.e., 3 < 5. The number 60 = 2^2*3*5 is not a term since q(60) > gpf(60), i.e., 7 > 5, etc.
Links
- Michael De Vlieger, Table of n, a(n) for n = 1..10000
Crossrefs
Programs
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Mathematica
f[x_] := Block[{q = 2}, While[Divisible[x, q], q = NextPrime[q]]; q]; Select[Range[256], Nor[Length[#2] == 1, Max[#2[[All, -1]]] == 1, Divisible[#1, Apply[Times, #2[[All, 1]]]^2], f[#1] > #2[[-1, 1]]] & @@ {#, FactorInteger[#]} &]