A334925 G.f.: Sum_{k>=1} x^(k*(k^2 + 1)/2) / (1 - x^(k*(k^2 + 1)/2)).
1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, 1, 1, 3, 1, 1, 2, 1, 2, 1, 1, 1, 1, 3, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2
Offset: 1
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Programs
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Mathematica
nmax = 100; CoefficientList[Series[Sum[x^(k (k^2 + 1)/2)/(1 - x^(k (k^2 + 1)/2)), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
Formula
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2 * (A248177 + A001620) = 1.343731... . - Amiram Eldar, Jan 02 2024
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