A074905 a(n) = number of terms in A030229 between prime(n) and prime(n+1).

0, 0, 1, 1, 0, 2, 0, 2, 1, 0, 3, 2, 0, 1, 1, 3, 0, 2, 1, 0, 2, 1, 3, 4, 0, 0, 1, 0, 1, 5, 1, 2, 0, 5, 0, 1, 3, 1, 0, 2, 0, 3, 0, 1, 0, 7, 7, 1, 0, 0, 2, 0, 2, 2, 2, 2, 0, 1, 1, 0, 2, 7, 1, 0, 1, 7, 2, 3, 0, 0, 2, 2, 1, 1, 2, 1, 5, 1, 2, 4, 0, 2, 0, 1, 0, 3, 3, 1, 1, 1, 4, 3, 1, 2, 2, 1, 6, 0, 6, 4, 3, 2, 2, 1, 1

Offset: 1

Author

Jani Melik, Sep 30 2002

Keywords

• nonn

Examples

			Between prime(6)=13 and prime(7)=17 there are two terms in A030229, namely 14 and 15, so a(6) = 2.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A030229, A061265, A061399.

Programs

Maple

readlib(issqr): sstmp := proc(n) local t1,i; t1 := 0; for i from ithprime(n) to ithprime(n+1) do if (issqrfree(i) = 'true' and mobius(i)=1) then t1 := t1+1; fi; od; t1; end: sstmp(200);

Mathematica

nt[{a_,b_}]:=Count[MoebiusMu[Range[a+1,b-1]],1]; nt/@Partition[Prime[ Range[ 110]],2,1] (* Harvey P. Dale, May 18 2021 *)

Extensions

Clarified definition, corrected offset, edited. - N. J. A. Sloane, May 18 2021