# [seqfan] Revision to A160763.

Robert G. Wilson, v rgwv at rgwv.com
Mon Jun 1 20:36:12 CEST 2009

```Dear Seq. Fans,                                           Ref:  A160763

Thank you for all of the help. I just sent to the OEIS an extensive
revision.

%I A160763
%S A160763 3,49,87,130321,4753,7212549413161,285541,7890946561,834472284661,
%T A160763 174913992535407978606601,19699251391,
%U A160763 23205949656945057666311162427422570380321
%N A160763 Least number having n divisors such that every sum of two or more divisors is composite.
%C A160763 First term of A093893 to have n divisors. a(2)=3, a(3)=7^2, a(4)=3*29, a(5)=19^4, a(6)=7*97, a(7)=139^6, a(8)=31*61*151, a(9)=211^2 * 421^2, a(10)=211^4 * 421, a(11)=211^10, a(12)=211^2 * 421 * 1051, a(13)=2311^12, a(14)<=2311^6 * 50821, a(15)<= 120121^4 * 150151^2, a(16)<=120121 * 150151 * 180181 * 270271, a(17)=120121^16, a(18)<= 4084081^2 * 5105101^2 * 8168161, a(19)=2312311^18, ..., .
%C A160763 The author wishes to thank Franklin T. Adams-Watters, Hagen von EItzen, Leroy Quet, Max Alekseyev, Maximilian F. Hasler, Maximilian F. Hasler and T. D. Noe for all of their help via the sequence fan list.
%t A160763 (* first do *) Needs["Combinatorica`"] (* then *) f[n_] := Block[{d = Divisors at n, k, mx}, k = 1 + Length at d; mx = 2^Length[d]; While[k < mx && !PrimeQ[Plus @@ NthSubset[k, d]], k++ ]; If[k == mx, Length at d, 0]]; t = Table[0, {20}]; k = 1; While[k < 2*107, a = f at k; If[a > 0 && t[[a]] == 0, t[[a]] = k; Print[{a, k}]]; k += 2]; t
%Y A160763 Cf. A093893, A000005.
%K A160763 hard,more,nonn,new
%O A160763 2,1
%A A160763 Robert G. Wilson v, May 25 2009, May 29 2009
%E A160763 Definition revised by njas, May 30 2009
%E A160763 Extensive revision by the author with much help. see the Comment line.

```