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A100832
Amenable numbers: n such that there exists a multiset of integers (s(1), ..., s(n)) whose size, sum and product are all n.
0
1, 5, 8, 9, 12, 13, 16, 17, 20, 21, 24, 25, 28, 29, 32, 33, 36, 37, 40, 41, 44, 45, 48, 49, 52, 53, 56, 57, 60, 61, 64, 65, 68, 69, 72, 73, 76, 77, 80, 81, 84, 85, 88, 89, 92, 93, 96, 97, 100, 101, 104, 105, 108, 109, 112, 113, 116, 117, 120, 121, 124, 125, 128, 129, 132
OFFSET
1,2
COMMENTS
Positive numbers k == 0 or 1 (mod 4), excluding k=4.
Essentially the same as A042948 (except 4 is not in this sequence).
The set {s(i)} is closed under multiplication. - Lekraj Beedassy, Jan 21 2005
LINKS
O. P. Lossers, Solution to problem 10454: Amenable Numbers, Amer. Math. Monthly Vol. 105 No. 4 April 1998.
Eric Weisstein's World of Mathematics, Amenable Number
Wikipedia, Amenable number
FORMULA
From Colin Barker, Jan 26 2012: (Start)
a(n) = a(n-1) + a(n-2) - a(n-3), n > 4.
G.f.: x*(1+3*x)*(1+x-x^2)/(1-x-x^2+x^3). (End)
EXAMPLE
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.
CROSSREFS
Sequence in context: A332245 A101079 A066812 * A314572 A034812 A260256
KEYWORD
nonn
AUTHOR
Lekraj Beedassy, Jan 07 2005
EXTENSIONS
More terms from David W. Wilson, Jan 24 2005
STATUS
approved