A369765 Maximal coefficient of (1 + x) * (1 + x^2) * (1 + x^3) * (1 + x^5) * ... * (1 + x^prime(n-1)).

1, 1, 1, 2, 2, 3, 3, 6, 7, 13, 19, 32, 53, 90, 156, 277, 494, 878, 1566, 2836, 5146, 9401, 17358, 32042, 59434, 110292, 204332, 380548, 713601, 1342448, 2538012, 4808578, 9043605, 17070234, 32268611, 61271738, 116123939, 220993892, 421000142, 802844420, 1534312896

Offset

0,4

Links

Table of n, a(n) for n=0..40.

Mathematica

Table[Max[CoefficientList[Product[(1 + x^If[k == 1, 1, Prime[k - 1]]), {k, 1, n}], x]], {n, 0, 40}]

Prog

(Python)
from collections import Counter
from sympy import prime
def A369765(n):
    c = {0:1, 1:1}
    for k in range(1, n):
        p, d = prime(k), Counter(c)
        for j in c:
            d[j+p] += c[j]
        c = d
    return max(c.values()) # Chai Wah Wu, Feb 01 2024

Crossrefs

Cf. A008578, A025591, A036497, A350457, A350514, A369708.

Sequence in context: A373446 A121211 A316585 * A146157 A238363 A255254

Adjacent sequences: A369762 A369763 A369764 * A369766 A369767 A369768

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 31 2024

Status

approved