The nth Cyclotomic polynomial, for any positive integer n, is the unique irreducible polynomial of largest degree with integer coefficients that is a divisor of x^n − 1, and is not a divisor of x^k − 1 for any k < n.



Task

 Find and print the first 30 cyclotomic polynomials.
 Find and print the order of the first 10 cyclotomic polynomials that have n or -n as a coefficient.


See also
 Wikipedia article, Cyclotomic polynomial, showing ways to calculate them.
 The sequence A013594 with the smallest order of cyclotomic polynomial containing n or -n as a coefficient.
with(NumberTheory):
for n to 30 do lprint(Phi(n,x)) od:
 
x-1
x+1
x^2+x+1
x^2+1
x^4+x^3+x^2+x+1
x^2-x+1
x^6+x^5+x^4+x^3+x^2+x+1
x^4+1
x^6+x^3+1
x^4-x^3+x^2-x+1
x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1
x^4-x^2+1
x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1
x^6-x^5+x^4-x^3+x^2-x+1
x^8-x^7+x^5-x^4+x^3-x+1
x^8+1
x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1
x^6-x^3+1
x^18+x^17+x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1
x^8-x^6+x^4-x^2+1
x^12-x^11+x^9-x^8+x^6-x^4+x^3-x+1
x^10-x^9+x^8-x^7+x^6-x^5+x^4-x^3+x^2-x+1
x^22+x^21+x^20+x^19+x^18+x^17+x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1
x^8-x^4+1
x^20+x^15+x^10+x^5+1
x^12-x^11+x^10-x^9+x^8-x^7+x^6-x^5+x^4-x^3+x^2-x+1
x^18+x^9+1
x^12-x^10+x^8-x^6+x^4-x^2+1
x^28+x^27+x^26+x^25+x^24+x^23+x^22+x^21+x^20+x^19+x^18+x^17+x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1
x^8+x^7-x^5-x^4-x^3+x+1
 
PhiSet:=[seq(map(abs,{coeffs(Phi(k,x),x)}),k=1..15000)]:
[seq(ListTools:-SelectFirst(s->member(n,s),PhiSet,output=indices),n=1..20)];
#[1, 105, 385, 1365, 1785, 2805, 3135, 6545, 6545, 10465, 10465, 
#  10465, 10465, 10465, 11305, 11305, 11305, 11305, 11305, 11305]