cp's OEIS Frontend

A327444 a(n) is the maximum absolute value of the coefficients of the quotient polynomial R_(prime(n)#)/Product_{j=1..n} R_(prime(j)), where prime(n)# is the n-th primorial number A002110(n) and R_k = (x^k - 1)/(x - 1).

%I A327444 #20 Sep 17 2019 09:43:23
%S A327444 1,1,2,4,7,20,34,93
%N A327444 a(n) is the maximum absolute value of the coefficients of the quotient polynomial R_(prime(n)#)/Product_{j=1..n} R_(prime(j)), where prime(n)# is the n-th primorial number A002110(n) and R_k = (x^k - 1)/(x - 1).
%C A327444 The values of the first few quotients, when x=10, are in A323060. (A file therein enumerates the coefficients of the fifth quotient.)
%C A327444 Conjecture: a(n) = exp((6n - 13 + (-1)^n)/8), approximately.
%e A327444 R_(510510)/[R_(2)*R_(3)*R_(5)*R_(7)*R_(11)*R_(13)*R_(17)] = 1 - 6x + 16x^2 - 25x^3 + ... - 34x^11313 + ... + x^510458 (and no other coefficient exceeds 34 in absolute value), so a(7) = 34.
%o A327444 (PARI) R(k) = (x^k - 1)/(x - 1);
%o A327444 a(n) = {my(v = Vec(R(prod(k=1, n, prime(k)))/prod(k=1, n, R(prime(k))))); vecmax(apply(x->abs(x), v));} \\ _Michel Marcus_, Sep 16 2019
%Y A327444 Cf. A002110, A323060.
%K A327444 nonn,more
%O A327444 1,3
%A A327444 _Patrick A. Thomas_, Sep 16 2019