A323049 Numbers that are neither 5-smooth nor a sum of two 5-smooth numbers.

71, 119, 142, 191, 211, 213, 223, 238, 239, 284, 299, 311, 319, 355, 357, 359, 367, 373, 382, 397, 419, 422, 426, 431, 446, 461, 463, 467, 473, 476, 478, 479, 497, 523, 529, 547, 551, 553, 559, 568, 569, 571, 573, 583, 589, 595, 598, 599, 607, 613, 617, 619, 622, 623, 638, 639, 659, 669, 671, 703, 709, 710, 713, 714

Offset: 1

Author

Carlos Alves, Jan 03 2019

Keywords

• nonn

Comments

Complementary set of (A323048).

Also numbers k such that at least three five-smooth numbers are needed to sum to k. - David A. Corneth, Jan 04 2019

Contains all k == 71 or 119 (mod 120). - Robert Israel, Apr 02 2019

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A003586, A051037, A323048.

Similar to A323046 (for 3-smooth numbers).

Programs

Maple

N:= 1000: # to get all terms <= N
V:= {seq(seq(seq(2^a*3^b*5^c, a = 0 .. floor(log[2](N/3^b/5^c))),b = 0 .. floor(log[3](N/5^c))),c=0..floor(log[5](N)))}:
S:= {$1..N} minus V minus {seq(seq(V[i]+V[j],i=1..j),j=1..nops(V))}:
A:= sort(convert(S,list)): # Robert Israel, Apr 02 2019

Mathematica

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)]}]; b = Block[{nn = 800, s}, s = f[nn]; {0, 1}~Join~
   Select[Union@Flatten@Outer[Plus, s, s], # <= nn &]];
Complement[Range[800], b]