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A308271
G.f. A(x) satisfies: A(x) = (1/(1 - x)) * A(x^2)*A(x^3)*A(x^5)* ... *A(x^prime(k))* ...
2
1, 1, 2, 3, 5, 7, 12, 16, 24, 33, 48, 64, 93, 122, 169, 224, 303, 395, 532, 686, 907, 1168, 1523, 1943, 2521, 3193, 4094, 5170, 6573, 8245, 10434, 13015, 16344, 20321, 25363, 31379, 39003, 48039, 59384, 72914, 89720, 109722, 134528, 163929, 200149, 243199, 295831, 358280
OFFSET
0,3
COMMENTS
Euler transform of A008480.
FORMULA
G.f.: Product_{k>=1} 1/(1 - x^k)^A008480(k).
MAPLE
g:= proc(n) option remember; (l-> add(i, i=l)!/
mul(i!, i=l))(map(i-> i[2], ifactors(n)[2]))
end:
a:= proc(n) option remember; `if`(n=0, 1, add(a(n-j)*
add(d*g(d), d=numtheory[divisors](j)), j=1..n)/n)
end:
seq(a(n), n=0..60); # Alois P. Heinz, May 17 2019
MATHEMATICA
terms = 47; A[_] = 1; Do[A[x_] = 1/(1 - x) Product[A[x^Prime[k]], {k, 1, terms}] + O[x]^(terms + 1) // Normal, terms + 1]; CoefficientList[A[x], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, May 17 2019
STATUS
approved