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A340534 a(n) is the least product of n consecutive primes that is divisible by the sum of those primes, or 0 if there is no such product.

%I A340534 #9 Jan 10 2021 22:11:38
%S A340534 2,0,30,0,15015,0,37182145,9699690,33426748355,0,3710369067405,0,
%T A340534 304250263527210,0,37420578814667938361329,0,
%U A340534 18598027670889965365580513,0,107254825578022430263302818471,0,44510752614879308559270669665465,0,267064515689275851355624017992790,0,116431182179248680450031658440253681535,0
%N A340534 a(n) is the least product of n consecutive primes that is divisible by the sum of those primes, or 0 if there is no such product.
%C A340534 a(27) > 10^225 if it is not 0.
%C A340534 If n is even, a(n) is either A002110(n) or 0.
%C A340534 a(n) = A002110(n) for n in A051838.
%e A340534 a(5) = 15015 = 3*5*7*11*13 is the product of 5 consecutive primes and is divisible by 3+5+7+11+13 = 39.
%p A340534 f:= proc(n) local L,i,p;
%p A340534    L:= [seq(ithprime(i),i=1..n)]:
%p A340534    p:= convert(L,`*`);
%p A340534    if n::even then
%p A340534      if p mod convert(L,`+`) = 0 then return p else return 0 fi
%p A340534    else
%p A340534      do
%p A340534        p:= convert(L,`*`);
%p A340534        if p mod convert(L,`+`) = 0 then return p fi;
%p A340534        if p > 10^225 then return FAIL fi;
%p A340534        L:= [op(L[2..-1]),nextprime(L[-1])];
%p A340534      od
%p A340534    fi;
%p A340534 end proc:
%p A340534 map(f, [$1..26]);
%Y A340534 Cf. A000210, A051838, A086487.
%K A340534 nonn
%O A340534 1,1
%A A340534 _J. M. Bergot_ and _Robert Israel_, Jan 10 2021