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A275001 Expansion of 1/(1 - Sum_{k>=1} x^(prime(k)^2)). 0

%I

%S 1,0,0,0,1,0,0,0,1,1,0,0,1,2,0,0,1,3,1,0,1,4,3,0,1,6,6,1,1,8,10,4,1,

%T 10,17,10,2,12,27,20,6,14,40,38,16,17,56,68,36,25,76,114,75,43,101,

%U 180,147,81,137,273,271,159,194,401,471,313,292,579,782,601,472,832,1251,1109,816

%N Expansion of 1/(1 - Sum_{k>=1} x^(prime(k)^2)).

%C Number of compositions (ordered partitions) of n into squares of primes (A001248).

%C From _Ilya Gutkovskiy_, Feb 12 2017: (Start)

%C Conjecture(1): every number > 23 is the sum of at most 8 squares of primes.

%C Conjecture(2): every number > 131 can be represented as a sum of 13 squares of primes. (End)

%H <a href="/index/Com#comp">Index entries for sequences related to compositions</a>

%H <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>

%F G.f.: 1/(1 - Sum_{k>=1} x^(prime(k)^2)).

%e a(17) = 3 because we have [4, 4, 9], [4, 9, 4] and [9, 4, 4].

%t nmax = 85; CoefficientList[Series[1/(1 - Sum[x^Prime[k]^2, {k, 1, nmax}]), {x, 0, nmax}], x]

%Y Cf. A001248, A006456, A023360, A090677.

%K nonn

%O 0,14

%A _Ilya Gutkovskiy_, Dec 24 2016

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Last modified February 18 15:33 EST 2018. Contains 299324 sequences. (Running on oeis4.)