A280242 Expansion of (Sum_{k>=2} floor(1/omega(k))*x^k)^2, where omega(k) is the number of distinct prime factors (A001221).

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

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: A235121 A270652 A326693 * A325953 A245343 A369858

Adjacent sequences: A280239 A280240 A280241 * A280243 A280244 A280245

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 29 2016

Status

approved