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

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

Author

Lekraj Beedassy, Jan 07 2005

Keywords

• nonn

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

Examples

			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.
		

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
• Index entries for linear recurrences with constant coefficients, signature (1, 1, -1).

Crossrefs

Cf. A014601, A042948.

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)

Extensions

More terms from David W. Wilson, Jan 24 2005