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 A282318 Number of ways of writing n as a sum of a prime and a nonprime squarefree number. 4
 0, 0, 0, 1, 1, 0, 1, 0, 2, 1, 0, 1, 2, 2, 1, 1, 1, 4, 2, 2, 2, 2, 1, 3, 3, 3, 2, 3, 3, 4, 1, 2, 4, 5, 2, 4, 2, 6, 5, 4, 4, 6, 3, 5, 6, 6, 4, 5, 3, 6, 3, 6, 5, 8, 3, 4, 4, 7, 6, 6, 4, 5, 8, 6, 6, 7, 2, 7, 9, 8, 5, 7, 6, 8, 8, 8, 8, 9, 3, 8, 9, 10, 8, 8, 5, 10, 6, 9, 10, 13, 4, 6, 8, 12, 10, 9, 8, 10, 12, 10, 9, 9, 7, 8, 11, 12, 9, 10 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,9 COMMENTS Conjecture: a(n) > 0 for all n > 10. LINKS Robert Israel, Table of n, a(n) for n = 0..10000 Ilya Gutkovskiy, Extended graphical example FORMULA G.f.: (Sum_{i>=1} x^prime(i))*(x + Sum_{j>=2} sgn(omega(j)-1)*mu(j)^2*x^j), where omega(j) is the number of distinct primes dividing j (A001221) and mu(j) is the Moebius function (A008683). EXAMPLE a(17) = 4 because we have [15, 2], [14, 3], [11, 6] and [10, 7]. MATHEMATICA nmax = 107; CoefficientList[Series[(Sum[x^Prime[i], {i, 1, nmax}]) (x + Sum[Sign[PrimeNu[j] - 1] MoebiusMu[j]^2 x^j, {j, 2, nmax}]), {x, 0, nmax}], x] PROG (MATLAB) N = 200; % to get a(0) to a(N) Primes = primes(N); B = zeros(1, N); B(Primes) = 1; LPrimes = Primes(Primes .^ 2 < N); SF = 1 - B; for p = LPrimes    SF(p^2:p^2:N) = 0; end C = conv(SF, B); C = [0, 0, C(1:N-1)] % Robert Israel, Feb 12 2017 CROSSREFS Cf. A001221, A000469, A008683, A098983. Sequence in context: A053616 A094718 A076191 * A286971 A025861 A090723 Adjacent sequences:  A282315 A282316 A282317 * A282319 A282320 A282321 KEYWORD nonn,look AUTHOR Ilya Gutkovskiy, Feb 11 2017 STATUS approved

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Last modified February 16 21:12 EST 2019. Contains 320199 sequences. (Running on oeis4.)