cp's OEIS Frontend

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.

Showing 1-3 of 3 results.

A036490 Numbers whose prime factors are in {5, 7, 11}.

Original entry on oeis.org

5, 7, 11, 25, 35, 49, 55, 77, 121, 125, 175, 245, 275, 343, 385, 539, 605, 625, 847, 875, 1225, 1331, 1375, 1715, 1925, 2401, 2695, 3025, 3125, 3773, 4235, 4375, 5929, 6125, 6655, 6875, 8575, 9317, 9625, 12005, 13475, 14641, 15125, 15625, 16807
Offset: 1

Views

Author

Olivier Gérard

Keywords

References

  • G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 160.

Links

Crossrefs

Cf. A036491, A036492.

Programs

  • Haskell
    import Data.Set (Set, fromList, insert, deleteFindMin)
a036490 n = a036490_list !! (n-1)
a036490_list = f $ fromList [5,7,11] where
   f s = m : (f $ insert (5 * m) $ insert (7 * m) $ insert (11 * m) s')
         where (m, s') = deleteFindMin s
-- Reinhard Zumkeller, Feb 19 2013
  • Mathematica
    Select[Range[20000], (fi = FactorInteger[#][[All, 1]]; Intersection[fi, {5, 7, 11}] == fi)&]
(* or, for a large number of terms: *)
f[pp_(* primes *), max_(* maximum term *)] := Module[{a, aa, k, iter}, k = Length[pp]; aa = Array[a, k]; iter = Table[{a[j], 0, PowerExpand @ Log[pp[[j]], max/Times @@ (Take[pp, j-1]^Take[aa, j-1])]}, {j, 1, k}]; Table[Times @@ (pp^aa), Sequence @@ iter // Evaluate] // Flatten // Sort]; A036490 = f[{5, 7, 11}, 2*10^14] // Rest (* Jean-François Alcover, Sep 19 2012, updated Nov 12 2016 *)

Formula

Sum_{n>=1} 1/a(n) = (5*7*11)/((5-1)*(7-1)*(11-1)) - 1 = 29/48. - Amiram Eldar, Sep 24 2020
a(n) ~ exp((6*log(5)*log(7)*log(11)*n)^(1/3)) / sqrt(385). - Vaclav Kotesovec, Sep 24 2020

Extensions

Offset corrected by Reinhard Zumkeller, Feb 19 2013

A036491 Transformation of A036490: 5^a*7^b*11^c -> 5^a*7^floor((b+2)/2)*11^c.

Original entry on oeis.org

5, 7, 11, 25, 35, 49, 55, 77, 121, 125, 175, 245, 275, 49, 385, 539, 605, 625, 847, 875, 1225, 1331, 1375, 245, 1925, 343, 2695, 3025, 3125, 539, 4235, 4375, 5929, 6125, 6655, 6875, 1225, 9317, 9625, 1715, 13475, 14641, 15125, 15625, 343, 2695, 21175
Offset: 1

Views

Author

Olivier Gérard

Keywords

References

  • G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 160.

Links

Crossrefs

Cf. A036490, A036492.

Programs

  • Haskell
    a036491 n = f z z where
   f x y | x `mod` 2401 == 0 = f (x `div` 49) (y `div` 7)
         | x `mod` 343 == 0  = y `div` 7
         | otherwise         = y
   z = a036490 n
-- Reinhard Zumkeller, Feb 19 2013
  • Mathematica
    f[pp_(*primes*), max_(*maximum term*)] := Module[{a, aa, k, iter}, k = Length[pp]; aa = Array[a, k]; iter = Table[{a[j], 0, PowerExpand @ Log[pp[[j]], max/Times @@ (Take[pp, j-1]^Take[aa, j-1])]}, {j, 1, k}]; Table[Times @@ (pp^aa), Sequence @@ iter // Evaluate] // Flatten // Sort]; A036490 = f[{5, 7, 11}, 2*10^14] // Rest; a[n_] := (a0 = A036490[[n]]; b = Max[1, IntegerExponent[a0, 7]]; 7^(Floor[(b+2)/2]-b) * a0); Table[a[n], {n, 1, Length[A036490]}]; (* Jean-François Alcover, Sep 19 2012, updated Nov 12 2016 *)

Extensions

Offset corrected by Reinhard Zumkeller, Feb 19 2013

A036484 a(n) is the minimal number of binary order n which has maximal number of divisors in this interval.

Original entry on oeis.org

1, 2, 4, 6, 12, 24, 60, 120, 240, 360, 840, 1680, 2520, 7560, 15120, 27720, 55440, 110880, 221760, 498960, 720720, 1441440, 3603600, 7207200, 14414400, 32432400, 61261200, 122522400, 245044800, 367567200, 735134400, 2095133040
Offset: 0

Views

Author

Labos Elemer

Keywords

Comments

Compare with A007416, where terms of this sequence are present.

Examples

			For n=9, with 256 < k <= 512, d(k) takes 17 distinct values, of which d(k)=24 is the greatest (see A036451 and A036470) and occurs first at k=360, so a(9)=360.

Crossrefs

Cf. A000005, A029837, A005179, A007416, A036470, A036492, A036493.

Programs

  • Mathematica
    Block[{nn = 22, s}, s = TakeList[Array[DivisorSigma[0, # + 1] &, 2^nn - 1], 2^Range[0, nn - 1]]; {1}~Join~Map[2^(#1 - 1) + #2 & @@ FirstPosition[s, #] &, Map[Max, s]]] (* Michael De Vlieger, Nov 04 2020 *)

Extensions

a(22)-a(31) from Sean A. Irvine, Nov 04 2020
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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