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A327444
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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).
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0
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OFFSET
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1,3
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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.
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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