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A133760
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Sum of the number of divisors of the numbers between prime(n) and prime(n+1).
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5
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0, 3, 4, 11, 6, 13, 6, 14, 25, 8, 27, 16, 8, 16, 29, 28, 12, 29, 18, 12, 28, 19, 32, 46, 21, 8, 20, 12, 22, 81, 20, 36, 8, 59, 12, 38, 34, 18, 39, 32, 18, 58, 14, 21, 12, 80, 70, 25, 12, 24, 34, 20, 56, 43, 34, 38, 16, 40, 26, 8, 65, 96, 24, 16, 22, 99, 40, 62, 12, 32, 30, 61, 40, 44
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = Sum_{j=prime(n)+1..prime(n+1)-1} A000005(j).
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EXAMPLE
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a(1) = 0 because there is no composite number between the primes 2 and 3.
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MAPLE
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A000005 := proc(n) numtheory[tau](n) ; end: A133760 := proc(n) add( A000005(i), i=ithprime(n)+1..ithprime(n+1)-1) ; end: seq(A133760(n), n=1..80);
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MATHEMATICA
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f[n_] := Plus @@ Flatten@ DivisorSigma[0, { Range[ Prime[n] + 1, Prime[n + 1] - 1]}]; Array[f, 74] (* Robert G. Wilson v, Jan 06 2008 *)
Total[DivisorSigma[0, Range[First[#]+1, Last[#]-1]]]&/@Partition[ Prime[ Range[ 80]], 2, 1] (* Harvey P. Dale, Jul 19 2013 *)
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PROG
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(PARI) a(n) = my(p=prime(n)); sum(k=p+1, nextprime(p+1)-1, numdiv(k)); \\ Michel Marcus, May 11 2022
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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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EXTENSIONS
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STATUS
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approved
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