The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A335261 Irregular triangle S(n,k) = denominators of k*A002110(n)/A005867(n) for 1 <= k <= A005867(n). 1
1, 1, 1, 1, 4, 2, 4, 1, 4, 2, 4, 1, 8, 4, 8, 2, 8, 4, 8, 1, 8, 4, 8, 2, 8, 4, 8, 1, 8, 4, 8, 2, 8, 4, 8, 1, 8, 4, 8, 2, 8, 4, 8, 1, 8, 4, 8, 2, 8, 4, 8, 1, 8, 4, 8, 2, 8, 4, 8, 1, 16, 8, 16, 4, 16, 8, 16, 2, 16, 8, 16, 4, 16, 8, 16, 1, 16, 8, 16, 4, 16, 8, 16 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,5
COMMENTS
Alternatively, denominators of k*A060753(n)/A038110(n) for 1 <= k <= A005867(n).
Let m = A038110(n). For row n, the primitive denominators d | m.
The mean of row n is related to the mean of row n of A309497: A060753(n+1)/(A038110(n+1)*2)) = 35/16 = Mean(A309497(n))/A038110(n+1).
LINKS
FORMULA
T(n,k) = m/GCD(k (mod m), m) with m = A038110(n).
Row lengths: A005867(n).
EXAMPLE
Table begins:
1;
1;
1, 1;
4, 2, 4, 1, 4, 2, 4, 1;
8, 4, 8, 2, 8, 4, 8, 1, ..., 8, 1;
...
Row n = 4 contains the denominators of (35/8)*k for 1 <= k <= A005867(4): 35/8, 35/4, 105/8, 35/2, 175/8, 105/4, 245/8, 35, 315/8, 175/4, 385/8, 105/2, 455/8, 245/4, 525/8, 70, 595/8, 315/4, 665/8, 175/2, 735/8, 385/4, 805/8, 105, 875/8, 455/4, 945/8, 245/2, 1015/8, 525/4, 1085/8, 140, 1155/8, 595/4, 1225/8, 315/2, 1295/8, 665/4, 1365/8, 175, 1435/8, 735/4, 1505/8, 385/2, 1575/8, 805/4, 1645/8, 210.
The mean of row 4: A060753(4+1)/(A038110(4+1)*2))* (A005867(4)+1) = (35/(8*2))*(48+1) = (35/16)*49 = 1715/16.
MATHEMATICA
Table[Denominator[P Range[EulerPhi[P]]/EulerPhi[P]], {P, FoldList[Times, Prime@ Range@ 5]}] (* or, more efficiently for larger datasets: *)
Flatten@ Block[{nn = 7, s, t}, s = Array[Numerator@ Product[1 - 1/Prime[k], {k, # - 1}] &, nn]; t = Nest[Append[#, #[[-1]] (Prime[Length@ #] - 1)]&, {1}, nn]; MapIndexed[Function[{m, D, i}, PadRight[{}, t[[i]], ReplacePart[ConstantArray[0, m], Flatten@ Map[Function[d, Map[# -> d &, m/d Select[Range[d], GCD[#, d] == 1 &]]], D]]]] @@ {#1, Divisors@ #1, First[#2]} &, s]]
(* or, to generate a single denominator of T(n, k) *)
f[n_, k_] := #/GCD[#, Mod[k, #]] &@ Numerator@ Product[1 - 1/Prime[i], {i, n - 1}]
CROSSREFS
Sequence in context: A156199 A135513 A176895 * A351864 A256789 A226577
KEYWORD
nonn,frac,easy,tabf
AUTHOR
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 5 01:34 EDT 2024. Contains 373102 sequences. (Running on oeis4.)