A193873 Smallest product of three distinct primes of the form n*k+1.

30, 105, 1729, 1105, 13981, 1729, 88537, 50881, 51319, 13981, 137149, 29341, 548497, 88537, 285541, 186337, 3372529, 51319, 18326641, 252601, 1152271, 137149, 1809641, 1366633, 3828001, 548497, 4814857, 645569, 4797703, 285541, 79230049, 4811297

Offset: 1

Author

Omar E. Pol, Sep 02 2011

Keywords

• nonn
• easy

Comments

Note that the Hardy-Ramanujan number is the first and the smallest repeated number: a(3) = a(6) = 1729.

Examples

			a(1) =  2*3*5 = 30
a(2) =  3*5*7 = 105
a(3) =  7*13*19 = 1729
a(4) =  5*13*17 = 1105
a(5) = 11*31*41 = 13981
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001235, A077316, A092609, A121940, A154729, A193869.

Programs

Mathematica

a[n_] := Module[{s = {}, c = 0, m = n + 1}, While[c < 3, While[!PrimeQ[m], m += n]; c++; AppendTo[s, m]; m += n]; Times @@ s]; Array[a, 100] (* Amiram Eldar, Jan 17 2025 *)

PARI

a(n)=my(p,q,k=1);while(!isprime(k+=n),);p=k;while(!isprime(k+=n),);q=k;while(!isprime(k+=n),);p*q*k \\ Charles R Greathouse IV, Sep 03 2011