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.
a033676 n = last $ takeWhile (<= a000196 n) $ a027750_row n -- Reinhard Zumkeller, Jun 04 2012
A033676 := proc(n) local a,d; a := 0 ; for d in numtheory[divisors](n) do if d^2 <= n then a := max(a,d) ; end if; end do: a; end proc: # R. J. Mathar, Aug 09 2009
largestDivisorLEQR[n_Integer] := Module[{dvs = Divisors[n]}, dvs[[Ceiling[Length@dvs/2]]]]; largestDivisorLEQR /@ Range[100] (* Borislav Stanimirov, Mar 28 2010 *)
Table[Last[Select[Divisors[n],#<=Sqrt[n]&]],{n,100}] (* Harvey P. Dale, Mar 17 2017 *)
A033676(n) = {local(d);if(n<2,1,d=divisors(n);d[(length(d)+1)\2])} \\ Michael B. Porter, Jan 30 2010
from sympy import divisors def A033676(n): d = divisors(n) return d[(len(d)-1)//2] # Chai Wah Wu, Apr 05 2021
isA := proc(n,s) if n mod s <> 0 then RETURN(false); fi; if n/s-s >= 0 then RETURN(true); else RETURN(false); fi; end: isA161344 := proc(n) for s from 3 to n do if isA(n,s) then RETURN(false); fi; od: isA(n,2) ; end: for n from 1 to 3000 do if isA161344(n) then printf("%d,",n) ; fi; od; # R. J. Mathar, Jun 24 2009
a[n_] := If[n <= 3, 2n+2, 2*Prime[n-1]]; Table[a[n], {n, 1, 56}] (* Jean-François Alcover, Nov 26 2012, after Zak Seidov *)
a(n)=if(n>3,prime(n-1),n+1)*2 \\ M. F. Hasler, Nov 27 2012
isA := proc(n,s) if n mod s <> 0 then RETURN(false); fi; if n/s-s >= 0 then RETURN(true); else RETURN(false); fi; end: isA161345 := proc(n) for s from 4 to n do if isA(n,s) then RETURN(false); fi; od: isA(n,3) ; end: for n from 1 to 3000 do if isA161345(n) then printf("%d,",n) ; fi; od; # R. J. Mathar, Jun 24 2009
md3Q[n_]:=Max[Select[Divisors[n],#<=Sqrt[n]&]]==3; Select[Range[800],md3Q] (* Harvey P. Dale, Aug 12 2013 *)
Array begins: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, ... 2, 6, 12, 20, 30, 42, 56, 72, 90, 110, 132, 156, ... 3, 8, 15, 24, 35, 48, 63, 80, 99, 120, 143, 168, ... 5, 10, 18, 28, 40, 54, 70, 88, 108, 130, 154, 180, ... 7, 14, 21, 32, 45, 60, 77, 96, 117, 140, 165, 192, ... 11, 22, 27, 44, 50, 66, 84, 104, 126, 150, 176, 204, ... 13, 26, 33, 52, 55, 78, 91, 112, 135, 160, 187, 216, ... 17, 34, 39, 68, 65, 102, 98, 128, 153, 170, 198, 228, ... 19, 38, 51, 76, 75, 114, 105, 136, 162, 190, 209, 264, ... 23, 46, 57, 92, 85, 138, 119, 152, 171, 200, 220, 276, ... 29, 58, 69, 116, 95, 174, 133, 184, 189, 230, 231, 348, ... 31, 62, 87, 124, 115, 186, 147, 232, 207, 250, 242, 372, ... ...
A163280 := proc(n,k) local r,T ; r := 0 ; for T from k^2 by k do if A033676(T) = k then r := r+1 ; if r = n then RETURN(T) ; fi; fi; od: end: # R. J. Mathar, Aug 09 2009
nmax = 12;
pm = Prime[nmax];
sDiv[n_] := Select[Divisors[n], #^2 <= n&][[-1]];
Clear[col]; col[k_] := col[k] = Select[Range[k pm], sDiv[#] == k&];
T[n_, k_ /; 1 <= k <= Length[col[k]]] := col[k][[n]];
Table[T[n-k+1, k], {n, 1, nmax}, {k, 1, n}] // Flatten (* Jean-François Alcover, Dec 15 2019 *)
isA := proc(n,s) if n mod s <> 0 then RETURN(false); fi; if n/s-s >= 0 then RETURN(true); else RETURN(false); fi; end: isA161424 := proc(n) for s from 5 to n do if isA(n,s) then RETURN(false); fi; od: isA(n,4) ; end: for n from 1 to 3000 do if isA161424(n) then printf("%d,",n) ; fi; od; # R. J. Mathar, Jun 24 2009
Select[Range[1, 1000], Function[m, Max[Select[Divisors[m], # <= Sqrt[m] &]] == 4]] (* Ashton Baker, Nov 03 2013 *)
From _Hartmut F. W. Hoft_, Sep 16 2015: (Start) a(23) = 52 = 2^2 * 13 = q * p with q = 4 in A174973 and 8 < 13 = p. a(59) = 136 = 2^3 * 17 = q * p with q = 8 in A174973 and 16 < 17 = p. The first six columns of the irregular triangle through prime 37: 1 2 4 6 8 12 ... ------------------------------- 3 5 10 7 14 11 22 44 13 26 52 78 17 34 68 102 136 19 38 76 114 152 23 46 92 138 184 29 58 116 174 232 348 31 62 124 186 248 372 37 74 148 222 296 444 ... (End)
isA174973 := proc(n) option remember; local k,dvs; dvs := sort(convert(numtheory[divisors](n),list)) ; for k from 2 to nops(dvs) do if op(k,dvs) > 2*op(k-1,dvs) then return false; end if; end do: true ; end proc: A174973 := proc(n) if n = 1 then 1; else for a from procname(n-1)+1 do if isA174973(a) then return a; end if; end do: end if; end proc: isA239929 := proc(n) local i,p,j,a73; for i from 1 do p := ithprime(i+1) ; if p > n then return false; end if; for j from 1 do a73 := A174973(j) ; if a73 > n then break; end if; if p > 2*a73 and n = p*a73 then return true; end if; end do: end do: end proc: for n from 1 to 200 do if isA239929(n) then printf("%d,",n) ; end if; end do: # R. J. Mathar, Oct 04 2018
(* sequence of numbers k for m <= k <= n having exactly two parts *) (* Function a237270[] is defined in A237270 *) a239929[m_, n_]:=Select[Range[m, n], Length[a237270[#]]==2&] a239929[1, 260] (* data *) (* Hartmut F. W. Hoft, Jul 07 2014 *) (* test for membership in A174973 *) a174973Q[n_]:=Module[{d=Divisors[n]}, Select[Rest[d] - 2 Most[d], #>0&]=={}] a174973[n_]:=Select[Range[n], a174973Q] (* compute numbers satisfying the condition *) a239929Stalk[start_, bound_]:=Module[{p=NextPrime[2 start], list={}}, While[start p<=bound, AppendTo[list, start p]; p=NextPrime[p]]; list] a239929F[n_]:=Sort[Flatten[Map[a239929Stalk[#, n]&, a174973[n]]]] a239929F[138] (* data *)(* Hartmut F. W. Hoft, Sep 16 2015 *)
Select[Range[1, 1000], Function[m, Max[Select[Divisors[m], # <= Sqrt[m] &]] == 4]] (* Ashton Baker, Nov 03 2013 *)
is(n)=divisors(n)[(numdiv(n)+1)\2]==5 \\ - M. F. Hasler, Nov 03 2013
A033676 := proc(n) local dvs; dvs := sort(convert(numtheory[divisors](n),list)) ; op(floor((nops(dvs)+1)/2) ,dvs) ; end: for n from 1 to 2000 do if A033676(n) = 7 then printf("%d,",n) ; fi; od: # R. J. Mathar, Jul 13 2009
ld = 7; selQ[n_] := AllTrue[Divisors[n], # <= ld || #^2 > n&]; Select[Range[ld, 200] ld, selQ] (* Jean-François Alcover, Apr 14 2020 *) ld7Q[n_]:=Select[Divisors[n],#<=Sqrt[n]&][[-1]]==7; Select[Range[1400],ld7Q] (* Harvey P. Dale, Jan 13 2023 *)
filter:= n -> andmap(t -> t<=10 or t^2 > n, numtheory:-divisors(n)): select(filter, [seq(n,n=100..10000,10)]); # Robert Israel, Aug 16 2018
ld10Q[n_]:=Last[Select[Divisors[n],#<=Sqrt[n]&]]==10; Select[Range[2000],ld10Q] (* Harvey P. Dale, Jan 30 2011 *)
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