cp's OEIS Frontend

A100832 Amenable numbers: n such that there exists a multiset of integers (s(1), ..., s(n)) whose size, sum and product are all n.

%I A100832 #29 Feb 16 2025 08:32:55
%S A100832 1,5,8,9,12,13,16,17,20,21,24,25,28,29,32,33,36,37,40,41,44,45,48,49,
%T A100832 52,53,56,57,60,61,64,65,68,69,72,73,76,77,80,81,84,85,88,89,92,93,96,
%U A100832 97,100,101,104,105,108,109,112,113,116,117,120,121,124,125,128,129,132
%N A100832 Amenable numbers: n such that there exists a multiset of integers (s(1), ..., s(n)) whose size, sum and product are all n.
%C A100832 Positive numbers k == 0 or 1 (mod 4), excluding k=4.
%C A100832 Essentially the same as A042948 (except 4 is not in this sequence).
%C A100832 The set {s(i)} is closed under multiplication. - _Lekraj Beedassy_, Jan 21 2005
%H A100832 O. P. Lossers, <a href="http://www.jstor.org/stable/2589724">Solution to problem 10454: Amenable Numbers</a>, Amer. Math. Monthly Vol. 105 No. 4 April 1998.
%H A100832 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AmenableNumber.html">Amenable Number</a>
%H A100832 Wikipedia, <a href="http://en.wikipedia.org/wiki/Amenable_number">Amenable number</a>
%H A100832 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1, 1, -1).
%F A100832 From _Colin Barker_, Jan 26 2012: (Start)
%F A100832 a(n) = a(n-1) + a(n-2) - a(n-3), n > 4.
%F A100832 G.f.: x*(1+3*x)*(1+x-x^2)/(1-x-x^2+x^3). (End)
%e A100832 5 and 8, for instance, are in the sequence because we have 5 = 1-1+1-1+5 = 1*(-1)*1*(-1)*5 and 8 = 1-1+1-1+1+1+2+4 = 1*(-1)*1*(-1)*1*1*2*4.
%Y A100832 Cf. A014601, A042948.
%K A100832 nonn
%O A100832 1,2
%A A100832 _Lekraj Beedassy_, Jan 07 2005
%E A100832 More terms from _David W. Wilson_, Jan 24 2005