A111700 Number of integers between p(n) and p(n+1) which are coprime to (p(n+1)-p(n)), where p(n) is the n-th prime.

0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 3, 1, 0, 1, 0, 1, 5, 1, 1, 0, 3, 0, 1, 1, 1, 1, 1, 0, 3, 0, 1, 0, 3, 3, 1, 0, 1, 1, 0, 3, 1, 1, 1, 0, 1, 1, 0, 3, 5, 1, 0, 1, 5, 1, 3, 0, 1, 1, 3, 1, 1, 1, 1, 3, 1, 3, 3, 0, 3, 0, 1, 1, 1, 3, 1, 0, 1, 3, 3, 1, 3, 1, 1, 3, 0, 5, 1

Offset

1,24

Links

Table of n, a(n) for n=1..100.

Formula

a(n) = phi(p(n+1)-p(n)) - 1, where phi(n) = A000010(n).

Example

Between the primes p(24) = 89 and p(25) = 97 are 3 integers (91, 93 and 95) which are coprime to (p(25)-p(24)) = 8, so a(24) = 3.

Mathematica

Table[EulerPhi[Prime[n + 1] - Prime[n]] - 1, {n, 1, 70}] (* Stefan Steinerberger, Mar 30 2006 *)

Prog

(MuPAD) for n from 2 to 100 do a := ithprime(n); b := nextprime(a+1); su := 0; for k from a+1 to b-1 do if gcd(k, (b-a)) = 1 then su := su+1; end_if; end_for; print(su); end_for; // Stefan Steinerberger

Crossrefs

Sequence in context: A120080 A227570 A352269 * A233316 A060096 A245756

Adjacent sequences: A111697 A111698 A111699 * A111701 A111702 A111703

Keyword

nonn

Author

Leroy Quet, Nov 17 2005

Extensions

More terms from Stefan Steinerberger, Nov 19 2005

Status

approved