This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A296095 #91 May 26 2025 18:26:37
%S A296095 3,4,5,7,8,9,10,11,12,13,16,17,18,19,20,21,25,26,27,28,29,31,32,34,36,
%T A296095 37,39,40,41,43,45,48,49,50,52,53,55,57,58,61,63,64,65,67,68,72,73,74,
%U A296095 75,76,79,80,81,82,84,85,89,90,91,93,97,98,100,101,103,104,106,108,109,111,112,113,116,117,121,122
%N A296095 Integers represented by cyclotomic binary forms.
%C A296095 Possibly a subsequence of A000401. - _C. S. Davis_, May 10 2025
%C A296095 All terms divisible by 11 appear to be either of the form 11^2*A383784(n) for n>1 or x^4 + u*x^3*y + x^2*y^2 + u*x*y^3 + y^4 for x>y>0 and u={-1, 1}. - _C. S. Davis_, May 14 2025
%H A296095 Peter Luschny, <a href="/A296095/b296095.txt">Table of n, a(n) for n = 1..1000</a> (terms 1..519 from Michel Waldschmidt).
%H A296095 Étienne Fouvry, Claude Levesque, and Michel Waldschmidt, <a href="https://arxiv.org/abs/1712.09019">Representation of integers by cyclotomic binary forms</a>, arXiv:1712.09019 [math.NT], 2017.
%p A296095 with(numtheory): for n from 3 to 1000 do F[n] := expand(y^phi(n)*cyclotomic(n, x/y)) od: for m to 1000 do for n from 3 to 50 do for x from -50 to 50 do for y from -50 to 50 do if `and`(F[n] = m, max(abs(x), abs(y)) > 1) then print(m); m := m+1; n := 3; x := -50; y := -50 end if end do end do end do end do;
%t A296095 isA296095[n_]:=
%t A296095 If[n<3, Return[False],
%t A296095 logn = Log[n]^1.161;
%t A296095 K = Floor[5.383*logn];
%t A296095 M = Floor[2*(n/3)^(1/2)];
%t A296095 k = 3;
%t A296095 While[True,
%t A296095 If[k==7,
%t A296095 K = Ceiling[4.864*logn];
%t A296095 M = Ceiling[2*(n/11)^(1/4)]
%t A296095 ];
%t A296095 For[y=2, y<=M, y++,
%t A296095 p[z_] = y^EulerPhi[k]*Cyclotomic[k,z];
%t A296095 For[x=1, x<=y, x++, If[n==p[x/y], Return[True]]]
%t A296095 ];
%t A296095 k++;
%t A296095 If[k>K, Break[]]
%t A296095 ];
%t A296095 Return[False]
%t A296095 ];
%t A296095 Select[Range[122], isA296095] (* _Jean-François Alcover_, Feb 20 2018, translated from _Peter Luschny_'s Sage script, updated Mar 01 2018 *)
%o A296095 (Sage)
%o A296095 def isA296095(n):
%o A296095 if n < 3: return False
%o A296095 logn = log(n)^1.161
%o A296095 K = floor(5.383*logn)
%o A296095 M = floor(2*(n/3)^(1/2))
%o A296095 k = 3
%o A296095 while True:
%o A296095 if k == 7:
%o A296095 K = ceil(4.864*logn)
%o A296095 M = ceil(2*(n/11)^(1/4))
%o A296095 for y in (2..M):
%o A296095 p = y^euler_phi(k)*cyclotomic_polynomial(k)
%o A296095 for x in (1..y):
%o A296095 if n == p(x/y): return True
%o A296095 k += 1
%o A296095 if k > K: break
%o A296095 return False
%o A296095 def A296095list(upto):
%o A296095 return [n for n in (1..upto) if isA296095(n)]
%o A296095 print(A296095list(122)) # _Peter Luschny_, Feb 28 2018
%o A296095 (Julia)
%o A296095 using Nemo
%o A296095 function isA296095(n)
%o A296095 n < 3 && return false
%o A296095 R, z = PolynomialRing(ZZ, "z")
%o A296095 N = QQ(n)
%o A296095 # Bounds from Fouvry, Levesque and Waldschmidt
%o A296095 logn = log(n)^1.161
%o A296095 K = Int(floor(5.383*logn))
%o A296095 M = Int(floor(2*(n/3)^(1/2)))
%o A296095 k = 3
%o A296095 while true
%o A296095 c = cyclotomic(k, z)
%o A296095 e = Int(eulerphi(ZZ(k)))
%o A296095 if k == 7
%o A296095 K = Int(ceil(4.864*logn))
%o A296095 M = Int(ceil(2*(n/11)^(1/4)))
%o A296095 end
%o A296095 for y in 2:M, x in 1:y
%o A296095 N == y^e*subst(c, QQ(x,y)) && return true
%o A296095 end
%o A296095 k += 1
%o A296095 k > K && break
%o A296095 end
%o A296095 return false
%o A296095 end
%o A296095 A296095list(upto) = [n for n in 1:upto if isA296095(n)]
%o A296095 println(A296095list(2040)) # _Peter Luschny_, Feb 28 2018
%Y A296095 Complement of A293654.
%Y A296095 Supersequence of A383784(n) for n>3, according to Proposition 6.2 of Fouvry et al.
%K A296095 nonn
%O A296095 1,1
%A A296095 _Michel Waldschmidt_, Feb 14 2018