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 A133760 Sum of the number of divisors of the numbers between prime(n) and prime(n+1). 5
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS David A. Corneth, Table of n, a(n) for n = 1..10000 FORMULA a(n) = Sum_{j=prime(n)+1..prime(n+1)-1} A000005(j). Sum_{j = 1..m} (a(j)+2) + 1 = A006218(prime(m+1) - 1). - David A. Corneth, May 11 2022 EXAMPLE a(1) = 0 because there is no composite number between the primes 2 and 3. a(4) = 11 = A000005(8)+A000005(9)+A000005(10), indices delimited by prime(4) = 7 and prime(5) = 11. MAPLE 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); MATHEMATICA 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 *) PROG (PARI) a(n) = my(p=prime(n)); sum(k=p+1, nextprime(p+1)-1, numdiv(k)); \\ Michel Marcus, May 11 2022 CROSSREFS Cf. A000005, A006218. Sequence in context: A290517 A295824 A180696 * A335887 A335888 A328851 Adjacent sequences: A133757 A133758 A133759 * A133761 A133762 A133763 KEYWORD easy,nonn AUTHOR Giovanni Teofilatto, Jan 05 2008 EXTENSIONS Edited, corrected and extended by Robert G. Wilson v and R. J. Mathar, Jan 06 2008 Name corrected by Jon Perry, Nov 23 2012 STATUS approved

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Last modified June 20 11:12 EDT 2024. Contains 373527 sequences. (Running on oeis4.)