A330486
Earliest start of a run of n numbers divisible by a seventh power larger than one.
Original entry on oeis.org
128, 76544, 2372890624, 390491792890623, 2083234733888734218749, 18962123650219836035505781245
Offset: 1
2372890624 is divisible by 2^7, 2372890625 is divisible by 5^7, 2372890626 is divisible by 3^7. This is the smallest number with this property, so a(3)=2372890624.
- J.-M. De Koninck, Those Fascinating Numbers, Entry 242, p. 63, Amer. Math. Soc., 2009.
A330483
Earliest start of a run of n numbers divisible by an eighth power larger than one.
Original entry on oeis.org
256, 636416, 70925781248, 36430999887109373, 5031679407516945387109374
Offset: 1
70925781248 is divisible by 2^8, 70925781249 is divisible by 3^8, 70925781250 is divisible by 5^8. This is the smallest number with this property, so a(3) = 70925781248.
A330480
Earliest start of a run of n numbers divisible by a fourth power larger than one.
Original entry on oeis.org
16, 80, 33614, 202099373, 40280549372, 430995495889374, 77405340617896874
Offset: 1
33614 is divisible by 7^4, 33615 is divisible by 3^4, and 33616 is divisible by 2^4. This is the smallest number with this property, so a(3)=33614.
- J.-M. De Koninck, Those Fascinating Numbers, Entry 242, p. 63, Amer. Math. Soc., 2009.
A330481
Earliest start of a run of n numbers divisible by a fifth power larger than one.
Original entry on oeis.org
32, 1215, 2590623, 2146909373, 105636978090621, 3269698976575137500
Offset: 1
1215 is divisible by 3^5 and 1216 is divisible by 2^5. This is the smallest number with this property, so a(2)=1215.
- J.-M. De Koninck, Those Fascinating Numbers, Entry 242, p. 63, Amer. Math. Soc., 2009.
A330482
Earliest start of a run of n numbers divisible by a sixth power larger than one.
Original entry on oeis.org
64, 16767, 26890623, 1507545109375, 777562026420218750, 283435321166212288109372
Offset: 1
26890623 is divisible by 3^6, 26890624 is divisible by 2^6, and 26890625 is divisible by 5^6. This is the smallest number with this property, so a(3) = 26890623.
- J.-M. De Koninck, Those Fascinating Numbers, Entry 242, p. 63, Amer. Math. Soc., 2009.
A330484
Earliest start of a run of n numbers divisible by a ninth power larger than one.
Original entry on oeis.org
512, 3995648, 2889212890624, 18705093636361328125, 19810215665260426138787109374
Offset: 1
2889212890624 is divisible by 2^9, 2889212890625 is divisible by 5^9, and 2889212890626 is divisible by 3^9. This is the smallest number with this property, so a(3)=2889212890624.
A330485
Earliest start of a run of n numbers divisible by a tenth power larger than one.
Original entry on oeis.org
1024, 24151040, 61938212890624, 9226967798833574218749, 13279660499584033124533574218748
Offset: 1
61938212890624 is divisible by 2^10, 61938212890625 is divisible by 5^10, and 61938212890626 is divisible by 3^10. This is the smallest number with this property, so a(3)=61938212890624.
A271444
Smallest of 4 consecutive numbers each divisible by a cube greater than one.
Original entry on oeis.org
22624, 355374, 885624, 912247, 1558248, 1642624, 1728375, 1761991, 2068373, 2485375, 2948373, 2987872, 3072248, 3073623, 3243750, 3571749, 3744872, 3772248, 3916374, 4231248, 4442877, 4503247, 4730373, 4757750, 5301125, 5344623, 5516125, 5812477, 6017247
Offset: 1
a(1)=22624 is the smallest cubeful number followed by other 3 cubeful numbers. They are divisible by 2^5, 5^3, 3^3, and 11^3, respectively.
-
cubQ[n_] := Max[Last /@ FactorInteger[n]] > 2; Select[Range[10^6], cubQ[#] && cubQ[# + 1] && cubQ[# + 2] && cubQ[# + 3] &]
SequencePosition[Table[If[AnyTrue[Rest[Divisors[n]],IntegerQ[CubeRoot[#]]&],1,0],{n,61*10^5}],{1,1,1,1}][[;;,1]] (* Harvey P. Dale, Jan 05 2025 *)
A271445
Smallest of 5 consecutive numbers each divisible by a cube.
Original entry on oeis.org
18035622, 100942496, 133799496, 146447622, 156406624, 185966872, 192779375, 215927748, 314066750, 327879871, 363664375, 377956500, 403254124, 412284624, 422615124, 440799246, 458147500, 520659248, 558732248, 562037373, 634965372, 642252750, 664596248
Offset: 1
a(1) = 18035622 is the smallest cubeful number followed by other 4 cubeful numbers. They are divisible by 3^4, 17^3, 2^3, 5^4, and 7^3, respectively.
A271446
Smallest of 6 consecutive numbers each divisible by a cube.
Original entry on oeis.org
4379776620, 6329354875, 16620507123, 54089484125, 55072893248, 66519175371, 68769514373, 80566783622, 87372290871, 91351389622, 99156598496, 105748687372, 112806598372, 114265205871, 117243671750, 148257477247, 155970667499, 174404710246, 177398391245
Offset: 1
a(1) = 4379776620 is the smallest cubeful number followed by other 5 cubeful numbers. They are divisible by 29^3, 11^3, 13^3, 3^3, 2^4, and 5^3, respectively.
Showing 1-10 of 13 results.
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