A100832 - OEIS

%I #28 Jul 03 2023 07:48:34

%S 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 52,53,56,57,60,61,64,65,68,69,72,73,76,77,80,81,84,85,88,89,92,93,96,

%U 97,100,101,104,105,108,109,112,113,116,117,120,121,124,125,128,129,132

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

%C Positive numbers k == 0 or 1 (mod 4), excluding k=4.

%C Essentially the same as A042948 (except 4 is not in this sequence).

%C The set {s(i)} is closed under multiplication. - _Lekraj Beedassy_, Jan 21 2005

%H 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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AmenableNumber.html">Amenable Number</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Amenable_number">Amenable number</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1, 1, -1).

%F From _Colin Barker_, Jan 26 2012: (Start)

%F a(n) = a(n-1) + a(n-2) - a(n-3), n > 4.

%F G.f.: x*(1+3*x)*(1+x-x^2)/(1-x-x^2+x^3). (End)

%e 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 Cf. A014601, A042948.

%K nonn

%O 1,2

%A _Lekraj Beedassy_, Jan 07 2005

%E More terms from _David W. Wilson_, Jan 24 2005