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URL: https://oeis.org/A280243

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A280243
Expansion of (Sum_{k>=2} floor(1/omega(k))*x^k)^3, where omega(k) is the number of distinct prime factors (A001221).
4
0, 0, 0, 0, 0, 0, 1, 3, 6, 10, 12, 15, 19, 24, 30, 34, 36, 39, 45, 45, 51, 52, 57, 66, 67, 66, 69, 73, 75, 87, 81, 87, 93, 94, 99, 111, 111, 126, 129, 130, 123, 141, 126, 156, 138, 150, 132, 168, 145, 168, 153, 172, 165, 195, 156, 189, 171, 202, 177, 228, 165, 225, 183, 225, 186, 243, 177, 243, 204, 238, 198
OFFSET
0,8
COMMENTS
Number of ordered ways of writing n as sum of three prime powers (1 excluded).
LINKS
Eric Weisstein's World of Mathematics, Prime Power
FORMULA
G.f.: (Sum_{k>=2} floor(1/omega(k))*x^k)^3.
EXAMPLE
a(7) = 3 because we have [3, 2, 2], [2, 3, 2] and [2, 2, 3].
MATHEMATICA
nmax = 70; CoefficientList[Series[(Sum[Floor[1/PrimeNu[k]] x^k, {k, 2, nmax}])^3, {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 29 2016
STATUS
approved