

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
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OFFSET

1,2


COMMENTS

Essentially the same as A042948.
The set {s(i)} is closed under multiplication.  Lekraj Beedassy, Jan 21 2005


REFERENCES

O. P. Lossers, Solution to problem 10454, "Amenable Numbers", Amer. Math. Monthly Vol. 105 No. 4 April 1998 MAA Washington DC.


LINKS

Table of n, a(n) for n=1..65.
Eric Weisstein's World of Mathematics, Amenable Number
Wikipedia, Amenable number


FORMULA

Consists of the numbers n == 0 or 1 (mod 4), excluding n=4.
a(n)=a(n1)+a(n2)a(n3), n>4. G.f.: x*(1+3*x)*(1+xx^2)/(1xx^2+x^3). [Colin Barker, Jan 26 2012]


EXAMPLE

5 and 8, for instance, are in the sequence because we have 5=11+11+5=1*(1)*1*(1)*5 and 8=11+11+1+1+2+4=1*(1)*1*(1)*1*1*2*4.


CROSSREFS

Cf. A014601.
Sequence in context: A191977 A101079 A066812 * A034812 A066467 A180244
Adjacent sequences: A100829 A100830 A100831 * A100833 A100834 A100835


KEYWORD

nonn


AUTHOR

Lekraj Beedassy, Jan 07 2005


EXTENSIONS

More terms from David W. Wilson, Jan 24 2005


STATUS

approved



