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
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).
A027566 Number of numbers not of form k_1 k_2 .. k_n (1/k_1 + .. + 1/k_n), k_i >= 1.
1, 18, 126, 1652
Offset: 2
A179797 Numbers not of the form abc + abd + acd + bcd, with 0 < a < b < c < d.
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, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75
Offset: 1
Comments
This sequence appears to contain 764 terms, ending with 181799. Complement of A179796.
Links
- T. D. Noe, Table of n, a(n) for n=1..764 (complete sequence)
- MathOverflow, A generalisation of the equation n = ab + ac + bc
Crossrefs
Cf. A027563 (which allows equality)
Programs
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Mathematica
nn=1000000; lim=Floor[nn^(1/3)]; cnt=Table[0,{nn}]; Do[k1=a*b*c; k2=a*b+a*c+b*c; d=0; While[d++; n=k1+k2*d; n<=nn, If[d!=a && d!=b && d!=c, cnt[[n]]=1]], {a,lim}, {b,a+1,Floor[Sqrt[nn/a]]}, {c,b+1,Floor[nn/a/b]}]; Flatten[Position[cnt,0]]
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