A327444 - OEIS

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).

1, 1, 2, 4, 7, 20, 34, 93

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OFFSET

1,3

COMMENTS

The values of the first few quotients, when x=10, are in A323060. (A file therein enumerates the coefficients of the fifth quotient.)

Conjecture: a(n) = exp((6n - 13 + (-1)^n)/8), approximately.

LINKS

Table of n, a(n) for n=1..8.

EXAMPLE

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.

PROG

(PARI) R(k) = (x^k - 1)/(x - 1);

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

CROSSREFS

Cf. A002110, A323060.

Sequence in context: A225435 A243049 A247234 * A291403 A101805 A145777

Adjacent sequences: A327441 A327442 A327443 * A327445 A327446 A327447

KEYWORD

nonn,more

AUTHOR

Patrick A. Thomas, Sep 16 2019

STATUS

approved