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A111751 Numbers n such that P(3*n + 1) has exactly two distinct prime factors, where P(m) is the partition number A000041. 0

%I

%S 2,22,25,28,37,40,60,73,78,80,129,135,158,162,215,220,228,238,269,285,

%T 315,332,344,347,355,365,366,390,397,402,439,443,470,477,533,549,653,

%U 694,710,715,716,745,765,782,822

%N Numbers n such that P(3*n + 1) has exactly two distinct prime factors, where P(m) is the partition number A000041.

%e If n=2 then P(3*n + 1) = 15 = 3 x 5 (two distinct prime factors), so the first term is 2.

%p with(combinat): with(numtheory): a:=proc(n) if nops(factorset(numbpart(3*n+1)))=2 then n else fi end: seq(a(n),n=1..300); # _Emeric Deutsch_, Jan 27 2006

%t For[n = 1, n < 550, n++, If[Length[FactorInteger[PartitionsP[3*n + 1]]] == 2, Print[n]]] (* _Stefan Steinerberger_, Jan 27 2006 *)

%Y Cf. A000041.

%K nonn

%O 1,1

%A _Parthasarathy Nambi_, Nov 19 2005

%E More terms from _Stefan Steinerberger_ and _Emeric Deutsch_, Jan 27 2006

%E More terms from _Emeric Deutsch_, Jan 30 2006

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Last modified October 23 08:40 EDT 2021. Contains 348211 sequences. (Running on oeis4.)