A383748 a(n) = q is the smallest integer, such that the numbers -1/q, i/q, -i/q with i = sqrt(-1), are three zeros of the polynomial P(A783747(n),z) = Sum_{k=1..r} d(k)*z^(k-1) where d(1) < d(2), ..., < d(r) are the r divisors of A383747(n).
2, 3, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 7, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 2, 3, 2, 3, 2, 2, 2, 3, 2, 11, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 3, 3, 2, 2, 3, 2, 2, 2, 2, 3, 2, 3, 2, 2, 2, 2, 3, 2, 2, 3, 13, 2, 3, 2, 2, 2, 2, 3, 2, 2
Offset: 1
Keywords
Examples
n q m = A783747(n) P(m,z) 3 zeros of P(m,z)
1 2 8 1+2z+4z^2+8z^3 -1/2, -i/2, i/2
2 3 27 1+3z+9z^2+27z^3 -1/3, -i/3, i/3
3 2 88 1+2z+4z^2+8z^3+11z^4+ -1/2, -i/2, i/2
22z^5+44z^6+88z^7
Programs
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Maple
with(numtheory) : A:=proc(n) local P, Q, i, q, d, ii: d:=divisors(n):P:=add(op(i,d)*x^(i-1),i=1..nops(d)): ii:=0:for q from 1 to n while (ii=0) do: Q:=(x+1/q)*(x^2+1/q^2): if divide(P,Q,'R') then ii:=1: A(n):=q:else fi:od:end proc: seq(A(n), n=1..2500);