A126105 Prime(n)^2*prime(n+1)...*prime(a(n)) is the least product of consecutive primes which is abundant. Note that only the first term is squared.

2, 5, 10, 20, 34, 50, 72, 97, 129, 165, 203, 248, 295, 346, 405, 469, 537, 607, 685, 766, 853, 949, 1049, 1155, 1264, 1376, 1494, 1620, 1754, 1897, 2048, 2193, 2346, 2503, 2669, 2836, 3012, 3193, 3378, 3572, 3770, 3973, 4186, 4400, 4624, 4855, 5098, 5339, 5578

Offset: 1

Author

Walter Kehowski, Mar 04 2007

Keywords

• less
• nonn

Examples

			a(3)=10 since x=5^2*7*11*13*17*19*23*29=5391411025 is abundant with sigma(x)=10799308800 and sigma(x)-2*x=16486750.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A005101, A007684 (a very similar sequence), A007708, A007741.

Programs

Mathematica

a[n_] := Module[{p = Prime[n]}, c = 1; pr = 1 + 1/p + 1/p^2; While[pr < 2, p = NextPrime[p]; pr *= (1 + 1/p); c++]; c + n - 1]; Array[a, 50] (* Amiram Eldar, Aug 14 2019 *)

Extensions

More terms from Stefan Steinerberger, May 11 2007

a(21) corrected and more terms added by Amiram Eldar, Aug 14 2019