

A280243


Expansion of (Sum_{k>=2} floor(1/omega(k))*x^k)^3, where omega(k) is the number of distinct prime factors (A001221).


3



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
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OFFSET

0,8


COMMENTS

Number of ordered ways of writing n as sum of three prime powers (1 excluded).


LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000
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

Cf. A001221, A098238, A246655.
Sequence in context: A319452 A187744 A007960 * A032732 A187352 A310044
Adjacent sequences: A280240 A280241 A280242 * A280244 A280245 A280246


KEYWORD

nonn


AUTHOR

Ilya Gutkovskiy, Dec 29 2016


STATUS

approved



