A323050 Numbers that cannot be written as a sum of two or fewer 7-smooth numbers (A002473).

311, 479, 551, 619, 622, 671, 719, 839, 851, 933, 937, 958, 1102, 1103, 1117, 1151, 1193, 1238, 1244, 1291, 1319, 1342, 1391, 1433, 1437, 1438, 1487, 1499, 1511, 1531, 1553, 1555, 1559, 1619, 1651, 1653, 1667, 1678, 1679, 1697, 1857, 1866, 1871, 1874, 1913, 1916, 1919, 1933, 1937, 1991, 2011, 2013, 2077, 2113, 2117, 2157

Offset: 1

Author

Carlos Alves, Jan 03 2019

Keywords

• nonn

Comments

Numbers that are not of the form (2^i * 3^j * 5^k * 7^l)*a + (2^m * 3^n * 5^p * 7^q)*b, with i,j,k,m,n,p >= 0, and a,b = 0 or 1. The first number excluded is 311.

These numbers are also included in A323046 and A323049.

Crossrefs

Similar to A323046 (for 3-smooth) and A323049 (for 5-smooth). Cf. A002473.

Programs

Mathematica

f[n_] := Union@Flatten@Table[2^a*3^b*5^c*7^d, {a, 0, Log2[n]}, {b, 0, Log[3, n/2^a]}, {c, 0, Log[5, n/(2^a*3^b)]}, {d, 0, Log[7, n/(2^a*3^b*5^c)]}];
b = Block[{nn = 3000, s}, s = f[nn]; {0, 1}~Join~Select[Union@Flatten@Outer[Plus, s, s], # <= nn &]];
Complement[Range[3000], b]