Factor a polynomial

Factor[x ^ 105 - 1]

(-1 + x)*(1 + x + x^2)*(1 + x + x^2 + x^3 + x^4)*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)*(1 - x + x^3 - x^4 + x^5 - x^7 + x^8)*(1 - x + x^3 - x^4 + x^6 - x^8 + x^9 - x^11 + x^12)*(1 - x + x^5 - x^6 + x^7 - x^8 + x^10 - x^11 + x^12 - x^13 + x^14 - x^16 + x^17 - x^18 + x^19 - x^23 + x^24)*(1 + x + x^2 - x^5 - x^6 - 2*x^7 - x^8 - x^9 + x^12 + x^13 + x^14 + x^15 + x^16 + x^17 - x^20 - x^22 - x^24 - x^26 - x^28 + x^31 + x^32 + x^33 + x^34 + x^35 + x^36 - x^39 - x^40 - 2*x^41 - x^42 - x^43 + x^46 + x^47 + x^48)

ListLinePlot[Table[Length[Factor[x ^ n - 1]], {n, 200}]]

-Graphics-