

A133760


Sum of the number of divisors of the numbers between prime(n) and prime(n+1).


1



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

Table of n, a(n) for n=1..74.


FORMULA

a(n) = sum_{ prime(n)<i<prime(n+1)} A000005(i).


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 *)
Total[DivisorSigma[0, Range[First[#]+1, Last[#]1]]]&/@Partition[ Prime[ Range[ 80]], 2, 1] (* Harvey P. Dale, Jul 19 2013 *)


CROSSREFS

Cf. A000005.
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



