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A331260 Denominator of harmonic mean of 3 consecutive primes. Numerators are A331259.

%I A331260 #11 Jul 29 2024 06:20:29
%S A331260 31,71,167,311,551,791,1151,1655,2279,3119,3935,4871,5711,6791,2797,
%T A331260 9959,11639,13175,14831,16559,18383,20975,24071,27419,30191,32231,
%U A331260 33911,36071,40511,45791,51983,55199,60167,64199,69599,24637,79031,84311,29917,94679
%N A331260 Denominator of harmonic mean of 3 consecutive primes. Numerators are A331259.
%H A331260 Robert Israel, <a href="/A331260/b331260.txt">Table of n, a(n) for n = 1..10000</a>
%F A331260 a(n) = denominator ((3*p1*p2*p3)/(p2*p3 + p1*p3 + p1*p2)) with p1 = prime(n), p2 = prime(n + 1), p3 = prime(n + 2).
%F A331260 a(n) = (p1*p2 + p1*p3 + p2*p3)/3 if p1 == p2 == p3 (mod 3), otherwise p1*p2 + p1*p3 + p2*p3. - _Robert Israel_, Jul 29 2024
%e A331260 See A331259.
%p A331260 P:= [seq(ithprime(i),i=1..102)]:
%p A331260 f:= proc(a,b,c) if nops({a,b,c} mod 3) = 1 then (a*b+a*c+b*c)/3 else a*b+a*c+b*c fi end proc;
%p A331260 [seq(f(P[i],P[i+1],P[i+2]),i=1..100)]; # _Robert Israel_, Jul 28 2024
%o A331260 (PARI) hm3(x, y, z)=3/(1/x+1/y+1/z);
%o A331260 p1=2; p2=3; forprime(p3=5, 190, print1(denominator(hm3(p1, p2, p3)), ", "); p1=p2; p2=p3)
%Y A331260 Cf. A046301, A127345, A292530, A331259.
%K A331260 nonn,frac,look
%O A331260 1,1
%A A331260 _Hugo Pfoertner_, Jan 19 2020