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%I #7 Jan 19 2020 09:19:31
%S 90,315,1155,3003,7293,12597,22287,38019,62031,99789,141081,195693,
%T 248583,321339,146969,572241,723399,870531,1041783,1228371,1435983,
%U 1750719,2149617,2615799,3027273,3339363,3603867,3953757,4692777,5639943,6837807,7483899,8512221
%N Numerator of harmonic mean of 3 consecutive primes. Denominators are A331260.
%F a(n) = numerator ((3*p1*p2*p3)/(p2*p3 + p1*p3 + p1*p2)) with p1 = prime(n), p2 = prime(n + 1), p3 = prime(n + 2).
%e b(1) = a(1)/A331260(1) = 3*2*3*5 / (3*5 + 2*5 + 2*3) = 90/31,
%e b(2) = a(2)/A331260(2) = 3*3*5*7 / (5*7 + 3*7 + 3*5) = 315/71,
%e ...
%e b(15) = a(15)/A331260(15) = 3*47*53*59 / (53*59 + 47*59 + 47*53) = 440907/8391 = 146969/2797. The common factor of 3 (see A292530) makes the denominator different from A127345(15).
%o (PARI) hm3(x,y,z)=3/(1/x+1/y+1/z);
%o p1=2; p2=3; forprime(p3=5,150, print1(numerator(hm3(p1,p2,p3)),", ");p1=p2;p2=p3)
%Y Cf. A046301, A127345, A292530, A331260.
%K nonn,frac
%O 1,1
%A _Hugo Pfoertner_, Jan 19 2020
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