A323048 Sums of no more than two 5-smooth numbers.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100

Offset: 1

Author

Carlos Alves, Jan 03 2019

Keywords

• nonn

Comments

Sequence includes 5-smooth numbers (A051037).

Numbers that are of the form (2^i * 3^j * 5^k)*a + (2^m * 3^n * 5^p)*b, with i,j,k,m,n,p >= 0, and a,b = 0 or 1. The first number excluded is 71. The numbers excluded are in A323049.

Examples

			70 = 2*2*3*5 + 2*5, 72 = 2*2*2*3*3 = 2*2*3*5 + 2*2*3, but 71 is not in the sequence.
		

Crossrefs

Cf. A051037, A323049 (complementary sequence).

Programs

Mathematica

S5 = Join[{0}, Select[Range[500], FactorInteger[#][[-1, 1]] <= 5 &]];
Union@Flatten@Outer[Plus, S5, S5]
(* more efficient code by Michael De Vlieger *)
f[n_] := Union@Flatten@Table[2^a*3^b*5^c, {a, 0, Log2[n]}, {b, 0, Log[3, n/2^a]}, {c, 0, Log[5, n/(2^a*3^b)]}]; Block[{nn = 500, s}, s = f[nn]; {0, 1}~Join~
  Select[Union@Flatten@Outer[Plus, s, s], # <= nn &]]

Extensions

Name edited by Jianing Song, Jun 11 2019