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A240590 Number of primes between successive powerful numbers (A001694(n)). 2

%I

%S 2,2,0,2,3,0,2,0,4,3,2,2,3,3,2,0,1,3,5,5,2,1,1,5,1,7,0,5,2,4,5,1,5,2,

%T 7,3,2,2,6,9,4,4,0,7,8,2,7,4,4,8,1,1,4,4,9,7,2,1,9,10,6,1,0,2,0,9,12,

%U 7,4,12,6,5,4,5,12,0,8,3,3,10,8,0,2,13,2,13,10,10,1,15,0,7,9,9,3,13,7,4,0,7,5,4,13,2

%N Number of primes between successive powerful numbers (A001694(n)).

%e a(9) = 4 because A001694(9) = 36, A001694(10) = 49, and there are 4 primes between them: 37, 41, 43 and 47.

%o (PARI)

%o ispowerful(n)={local(h);if(n==1,h=1,h=(vecmin(factor(n)[, 2])>1));return(h)}

%o proxpowerful(n)={local(k);k=n+1;while(!ispowerful(k),k+=1);return(k)}

%o {for(i=1,5000,if(ispowerful(i),m=proxpowerful(i);p=primepi(m)-primepi(i);print(p)))}

%Y Cf. A001694, A240591.

%K nonn

%O 1,1

%A _Antonio Roldán_, Apr 08 2014

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Last modified October 18 07:42 EDT 2019. Contains 328146 sequences. (Running on oeis4.)