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A116357
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Number of partitions of n into products of two successive primes (A006094).
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5
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0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 1, 0, 1, 2, 0, 0, 1, 0, 1, 2, 0, 0, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 3, 0, 1, 2, 0, 2, 3, 0, 1, 2, 1, 2, 3, 0, 1, 3, 1, 3, 3, 0, 2, 3, 1, 3, 3, 1, 2, 3, 1, 3, 4, 1, 3, 3, 1, 4, 4, 1, 3, 3, 2, 4, 4, 1, 3, 5
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OFFSET
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1,30
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COMMENTS
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LINKS
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FORMULA
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G.f.: Product_{k >= 1} 1/(1 - x^(prime(k)*prime(k+1)}). - Robert Israel, Dec 09 2016
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EXAMPLE
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a(41) = #{2*3 + 5*7} = 1;
a(42) = #{2*3+2*3+2*3+2*3+2*3+2*3+2*3, 2*3+2*3+3*5+3*5} = 2.
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MAPLE
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N:= 200: # to get a(1) to a(N)
Primes:= select(isprime, [2, seq(i, i=3..1+floor(sqrt(N)), 2)]):
G:= mul(1/(1 - x^(Primes[i]*Primes[i+1])), i=1..nops(Primes)-1):
S:= series(G, x, N+1):
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MATHEMATICA
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m = 105; kmax = PrimePi[Sqrt[m]]; Product[1/(1-x^(Prime[k]*Prime[k+1])), {k, 1, kmax}] + O[x]^(m+1) // CoefficientList[#, x]& // Rest (* Jean-François Alcover, Mar 09 2019, after Robert Israel *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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