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

1,1

Links

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

Example

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.

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 *)

Crossrefs

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

Sequence in context: A039690 A243938 A365630 * A117486 A263002 A325649

Adjacent sequences: A126102 A126103 A126104 * A126106 A126107 A126108

Keyword

less,nonn

Author

Walter Kehowski, Mar 04 2007

Extensions

More terms from Stefan Steinerberger, May 11 2007

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

Status

approved