cp's OEIS Frontend

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).

%I A383748 #10 May 16 2025 18:51:48
%S A383748 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,
%T A383748 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,
%U A383748 3,2,2,2,2,3,2,2,3,13,2,3,2,2,2,2,3,2,2
%N 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).
%e A383748  n  q  m = A783747(n)         P(m,z)          3 zeros of P(m,z)
%e A383748  1  2       8          1+2z+4z^2+8z^3         -1/2, -i/2, i/2
%e A383748  2  3      27          1+3z+9z^2+27z^3        -1/3, -i/3, i/3
%e A383748  3  2      88          1+2z+4z^2+8z^3+11z^4+  -1/2, -i/2, i/2
%e A383748                        22z^5+44z^6+88z^7
%p A383748 with(numtheory) :
%p A383748 A:=proc(n) local P, Q, i, q, d, ii:
%p A383748 d:=divisors(n):P:=add(op(i,d)*x^(i-1),i=1..nops(d)):
%p A383748 ii:=0:for q from 1 to n while (ii=0) do:
%p A383748 Q:=(x+1/q)*(x^2+1/q^2):
%p A383748 if divide(P,Q,'R') then ii:=1:
%p A383748 A(n):=q:else fi:od:end proc:
%p A383748 seq(A(n), n=1..2500);
%Y A383748 Cf. A027750, A291127, A383747.
%K A383748 nonn
%O A383748 1,1
%A A383748 _Michel Lagneau_, May 08 2025