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.

2, 0, 30, 0, 15015, 0, 37182145, 9699690, 33426748355, 0, 3710369067405, 0, 304250263527210, 0, 37420578814667938361329, 0, 18598027670889965365580513, 0, 107254825578022430263302818471, 0, 44510752614879308559270669665465, 0, 267064515689275851355624017992790, 0, 116431182179248680450031658440253681535, 0

Offset: 1

Author

J. M. Bergot and Robert Israel, Jan 10 2021

Keywords

• nonn

Comments

a(27) > 10^225 if it is not 0.

If n is even, a(n) is either A002110(n) or 0.

a(n) = A002110(n) for n in A051838.

Examples

			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.
		

Crossrefs

Cf. A000210, A051838, A086487.

Programs

Maple

f:= proc(n) local L,i,p;
   L:= [seq(ithprime(i),i=1..n)]:
   p:= convert(L,`*`);
   if n::even then
     if p mod convert(L,`+`) = 0 then return p else return 0 fi
   else
     do
       p:= convert(L,`*`);
       if p mod convert(L,`+`) = 0 then return p fi;
       if p > 10^225 then return FAIL fi;
       L:= [op(L[2..-1]),nextprime(L[-1])];
     od
   fi;
end proc:
map(f, [$1..26]);