

A280242


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


3



0, 0, 0, 0, 1, 2, 3, 4, 3, 4, 5, 6, 6, 6, 5, 6, 7, 4, 7, 6, 8, 8, 7, 4, 8, 6, 7, 8, 8, 6, 10, 6, 11, 8, 13, 8, 14, 4, 9, 8, 12, 6, 10, 6, 10, 10, 11, 4, 14, 6, 13, 8, 12, 4, 15, 6, 14, 8, 11, 4, 14, 6, 11, 8, 13, 4, 18, 4, 14, 10, 14, 4, 18, 6, 13, 12, 14, 6, 18, 4, 16, 8, 11, 8, 20, 6, 17, 8, 14, 6, 22, 8, 16, 6, 13, 4, 20, 4
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OFFSET

0,6


COMMENTS

Number of ordered ways of writing n as the sum of two 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)^2.


EXAMPLE

a(6) = 3 because we have [4, 2], [3, 3] and [2, 4].


MATHEMATICA

nmax = 97; CoefficientList[Series[(Sum[Floor[1/PrimeNu[k]] x^k, {k, 2, nmax}])^2, {x, 0, nmax}], x]


CROSSREFS

Cf. A001221, A071330, A071331, A073610, A095840, A246655.
Sequence in context: A123066 A235121 A270652 * A245343 A255938 A081748
Adjacent sequences: A280239 A280240 A280241 * A280243 A280244 A280245


KEYWORD

nonn


AUTHOR

Ilya Gutkovskiy, Dec 29 2016


STATUS

approved



