A025052 Numbers not of form ab + bc + ca for 1<=a<=b<=c (probably the list is complete).
1, 2, 4, 6, 10, 18, 22, 30, 42, 58, 70, 78, 102, 130, 190, 210, 330, 462
Offset: 1
A027563 Numbers not of form abc + abd + acd + bcd for 1<=a<=b<=c<=d.
1, 2, 3, 5, 6, 8, 9, 11, 14, 15, 18, 21, 23, 26, 29, 30, 33, 35, 41, 48, 51, 53, 63, 65, 74, 75, 86, 89, 90, 98, 111, 113, 119, 125, 131, 141, 155, 158, 173, 179, 191, 209, 210, 233, 239, 251, 254, 273, 285, 293, 321, 323, 326, 338, 341, 345, 363, 419
Offset: 1
Comments
This list is conjecturally complete, but this has not been proved. It may be complete as a consequence of the Generalized Riemann Hypothesis; see comments for A025052. - Harry Richman, Jan 09 2025
Links
- T. D. Noe, Table of n, a(n) for n=1..126 (complete sequence)
A027564 Numbers not of form abcd + abce + abde + acde + bcde for 1 <= a <= b <= c <= d <= e.
1, 2, 3, 4, 6, 7, 8, 10, 11, 12, 14, 15, 18, 19, 20, 22, 24, 26, 27, 31, 32, 34, 35, 36, 38, 39, 42, 46, 47, 50, 54, 55, 59, 60, 62, 66, 67, 70, 71, 75, 78, 84, 87, 90, 92, 94, 98, 99, 102, 104, 106, 110, 111, 115, 116, 119, 122, 126, 127, 130, 131, 132, 138
Offset: 1
Links
- Robert Israel, Table of n, a(n) for n = 1..1578
Programs
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Maple
N := 1000: # for all terms <= N V:= Vector(N): for a from 1 to floor((N/5)^(1/4)) do for b from a while 4*a*b^3+b^4<= N do for c from b while 3*a*b*c^2 + (a+b)*c^3 <= N do for d from c while 2*a*b*c*d + (b*c+a*c+a*b)*d^2 <= N do for e from d do r:= a*b*c*d+a*b*c*e+a*b*d*e+a*c*d*e+b*c*d*e; if r > N then break fi; V[r]:= 1; od od od od od: select(t -> V[t]=0, [$1..N]); # Robert Israel, Nov 04 2018
A027565 Largest number not of form k_1 k_2 .. k_n (1/k_1 + .. + 1/k_n), k_i integers >= 1.
1, 462, 52061, 33952307
Offset: 2
Examples
For n=2, the largest number not of the form k_1+k_2 with k_1>=1, k_2>=1 is 1! So a(2) = 1. For n=3 the largest number not of the form ab+bc+ca (a,b,c >= 1) is believed to be 462 (see A025052).
Comments
Links
Crossrefs
Programs
Mathematica
n=500; lim=Ceiling[(n-1)/2]; lst={}; Do[m=a*b+a*c+b*c; If[m<=n, lst=Union[lst, {m}]], {a, lim}, {b, lim}, {c, lim}]; Complement[Range[n], lst]Extensions