A194262 - OEIS

%I #21 May 30 2015 22:09:56

%S 1,2,3,5,7,11,1,1,1,1,1,1,101,1,1,1,1,1,1,19,1,167,251,1,89,29,43,13,

%T 83,467,311,23,1,1231,41,17977,281,1,1,127,193,2417,71,97,1087,241,67,

%U 7013,631,9283,661,53,5237,59,227,1019,102359,3251,199,409,971

%N Largest prime that divides the n-th partition number p(n) but does not divide p(1)*p(2)*...*p(n-1), or 1 if none.

%C It appears that a(n) is prime for all n > 97. See A194259 and A194260 for additional comments and links.

%H Alois P. Heinz and Giovanni Resta, <a href="/A194262/b194262.txt">Table of n, a(n) for n = 1..10000</a> (first 2000 terms from Alois P. Heinz)

%p with(combinat): with(numtheory):

%p b:= proc(n) option remember;

%p       `if`(n=1, {}, b(n-1) union factorset(numbpart(n)))

%p     end:

%p a:= n-> `if`(n=1, 1, max(1, (b(n) minus b(n-1))[])):

%p seq(a(n), n=1..120);  # _Alois P. Heinz_, Aug 21 2011

%t a[n_] := Complement[FactorInteger[PartitionsP[n]][[All, 1]], FactorInteger[Product[PartitionsP[k], {k, 1, n-1}]][[All, 1]]] /. {} -> {1} // Last; Table[a[n], {n, 1, 100}] (* _Jean-François Alcover_, Jan 28 2014 *)

%Y Cf. A000041, A071963, A194259, A194260, A194261.

%K nonn,look

%O 1,2

%A _Jonathan Sondow_, Aug 21 2011