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Number of integers with an odd number of distinct primes (for which mu(n)=-1) between two consecutive primes prime(n) and prime(n+1).
0

%I #3 Mar 31 2012 14:39:59

%S 2,2,2,2,2,2,2,2,2,3,2,2,3,2,2,2,2,3,3,2,3,2,2,2,2,3,3,2,3,3,3,2,3,2,

%T 2,3,2,3,3,3,2,5,2,3,2,2,3,2,2,4,3,2,3,3,3,3,2,3,2,3,5,2,3,2,2,4,2,3,

%U 2,2,4,3,3,3,2,3,2,3,4,4,2,5,2,5,3,2,3,2,2,3,4,3,2,4,2,3,3,2,4,2,3,3,2,2,3

%N Number of integers with an odd number of distinct primes (for which mu(n)=-1) between two consecutive primes prime(n) and prime(n+1).

%e Between 7919 and 7927 the 5 numbers which have an odd number of distinct primes are as follows: {7919,7922,7923,7926,7927}, so a(1000)=5.

%p readlib(issqr): lstmp := 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: lstmp(200);

%Y Cf. A061265, A061399.

%K nonn

%O 0,1

%A _Jani Melik_, Sep 30 2002