A193869 Smallest product of n distinct primes of the form n*k + 1.

2, 15, 1729, 32045, 60551711, 85276009, 52814801041129, 1312422595226609, 1130308388231798179, 4182230628909121261, 100166053986652515419641469, 1898732717895963155960377, 1011844196551535741726366525322443

Offset: 1

Author

Omar E. Pol, Sep 01 2011

Keywords

• nonn

Comments

Also the row products of triangle A077316.

Note that a(3) = 1729 is known as the Hardy-Ramanujan number.

Examples

			a(1) = 2
a(2) = 3*5 = 15
a(3) = 7*13*19 = 1729
a(4) = 5*13*17*29 = 32045
a(5) = 11*31*41*61*71 = 60551711
a(6) = 7*13*19*31*37*43 = 85276009
		

Links

• Nathaniel Johnston, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A001235, A077316, A092609, A121940, A154729.

Programs

Maple

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

Extensions

a(7)-a(14) from Nathaniel Johnston, Sep 02 2011