|
%I #18 Apr 01 2019 02:27:08
%S 2,15,1729,32045,60551711,85276009,52814801041129,1312422595226609,
%T 1130308388231798179,4182230628909121261,100166053986652515419641469,
%U 1898732717895963155960377,1011844196551535741726366525322443
%N Smallest product of n distinct primes of the form n*k + 1.
%C Also the row products of triangle A077316.
%C Note that a(3) = 1729 is known as the Hardy-Ramanujan number.
%H Nathaniel Johnston, <a href="/A193869/b193869.txt">Table of n, a(n) for n = 1..100</a>
%e a(1) = 2
%e a(2) = 3*5 = 15
%e a(3) = 7*13*19 = 1729
%e a(4) = 5*13*17*29 = 32045
%e a(5) = 11*31*41*61*71 = 60551711
%e a(6) = 7*13*19*31*37*43 = 85276009
%p Tj := proc(n,k) option remember: local j,p: if(k=0)then return 0:fi: for j from procname(n,k-1)+1 do if(isprime(n*j+1))then return j: fi: od: end: A193869 := proc(n) return mul(n*Tj(n,k)+1,k=1..n): end: seq(A193869(n),n=1..15); # _Nathaniel Johnston_, Sep 02 2011
%Y Cf. A001235, A077316, A092609, A121940, A154729.
%K nonn
%O 1,1
%A _Omar E. Pol_, Sep 01 2011
%E a(7)-a(14) from _Nathaniel Johnston_, Sep 02 2011
| 