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%I #6 Jan 04 2019 09:03:41
%S 1,2,0,4,0,4,0,0,0,2,0,4,0,0,0,6,0,6,0,0,0,4,0,0,0,0,0,2,0,14,0,0,0,0,
%T 0,6,0,0,0,6,0,10,0,0,0,12,0,0,0,0,0,2,0,0,0,0,0,6,0,2,0,0,0,0,0,14,0,
%U 0,0,4,0,8,0,0,0,0,0,4,0,0,0,10,0,0,0,0,0,4,0,0,0,0,0,0,0,6,0,0,0,6,0,6,0,0
%N a(n) = (pi(n+1)-pi(n)) * (prime(n+1)-prime(n)), where pi(k) is the number of prime numbers less than or equal to k (= A000720(k)) and prime(k) is the k-th prime number (= A000040(k)).
%H Antti Karttunen, <a href="/A109578/b109578.txt">Table of n, a(n) for n = 1..20000</a>
%F a(n) = (A010051(1+n) * A001223(n)). - _Antti Karttunen_, Jan 03 2019
%p with(numtheory): a:=n->(pi(n+1)-pi(n))*(ithprime(n+1)-ithprime(n)): seq(a(n),n=1..160);
%t an = Table[(PrimePi[n + 1] - PrimePi[n])*(Prime[n + 1] - Prime[n]), {n, 1, 200}]
%o (PARI) A109578(n) = ((primepi(n+1)-primepi(n)) * (prime(n+1)-prime(n))); \\ _Antti Karttunen_, Jan 03 2019
%Y Cf. A001223, A010051.
%Y Cf. also A096500, A096501.
%K nonn
%O 1,2
%A _Roger L. Bagula_, Jun 29 2005
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