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A339558
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Number of divisors of 2n that are the average of a pair of twin primes.
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1
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0, 1, 1, 1, 0, 3, 0, 1, 2, 1, 0, 3, 0, 1, 2, 1, 0, 4, 0, 1, 2, 1, 0, 3, 0, 1, 2, 1, 0, 5, 0, 1, 1, 1, 0, 5, 0, 1, 1, 1, 0, 4, 0, 1, 3, 1, 0, 3, 0, 1, 2, 1, 0, 5, 0, 1, 1, 1, 0, 5, 0, 1, 3, 1, 0, 3, 0, 1, 2, 1, 0, 5, 0, 1, 3, 1, 0, 3, 0, 1, 2, 1, 0, 4, 0, 1, 1, 1, 0, 7, 0
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OFFSET
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1,6
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LINKS
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FORMULA
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a(n) = Sum_{d|(2*n)} c(d+1) * c(d-1), where c is the prime characteristic (A010051).
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EXAMPLE
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a(6) = 3; There are 3 divisors of 2*6 = 12 that are the average of twin primes, namely 4, 6 and 12.
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MAPLE
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f:= proc(n) nops(select(t -> isprime(t-1) and isprime(t+1), numtheory:-divisors(2*n))) end proc:
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MATHEMATICA
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Table[Sum[(PrimePi[2n/i + 1] - PrimePi[2n/i]) (PrimePi[2n/i - 1] - PrimePi[2n/i - 2]) (1 - Ceiling[2n/i] + Floor[2n/i]), {i, 2n}], {n, 100}]
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PROG
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(PARI) a(n) = sumdiv(2*n, d, (d>1) && (bigomega(d^2-1)==2)); \\ Michel Marcus, Dec 16 2020
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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