A376384 Numbers k such that there exists at least two m <= k such that both rad(m) | k and m is neither squarefree nor a prime power, i.e., m is in A126706, where rad = A007947.
18, 24, 30, 36, 40, 42, 48, 50, 54, 56, 60, 66, 70, 72, 75, 78, 80, 84, 88, 90, 96, 98, 100, 102, 104, 105, 108, 110, 112, 114, 120, 126, 130, 132, 135, 136, 138, 140, 144, 147, 150, 152, 154, 156, 160, 162, 165, 168, 170, 174, 176, 180, 182, 184, 186, 189, 190
Offset: 1
Examples
Table showing the intersection of A126706 and row a(n) of A162306 for n = 1..12:
18: {12, 18},
24: {12, 18, 24},
30: {12, 18, 20, 24},
36: {12, 18, 24, 36},
40: {20, 40},
42: {12, 18, 24, 28, 36},
48: {12, 18, 24, 36, 48},
50: {20, 40, 50},
54: {12, 18, 24, 36, 48, 54},
56: {28, 56},
60: {12, 18, 20, 24, 36, 40, 45, 48, 50, 54, 60},
66: {12, 18, 24, 36, 44, 48, 54}.
Links
- Michael De Vlieger, Table of n, a(n) for n = 1..10000
- Michael De Vlieger, Hasse diagrams of row a(n) of A162306 for n = 1..12, showing numbers m in A126706 in blue, primes in red, perfect prime powers in gold, and squarefree composites in green.
Programs
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Mathematica
Select[Range[2^8], Function[n, 1 < Count[Range[n], _?(And[Divisible[n, Times @@ FactorInteger[#][[All, 1]]], Nor[SquareFreeQ[#], PrimePowerQ[#]]] &)] ] ]
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