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 1-10 of 11 results. Next

A112822 Least number k such that lcm{1,2,...,k}/denominator of harmonic number H(k) = 2n-1.

Original entry on oeis.org

1, 6, 105, 44, 63, 33, 156, 20, 272, 343, 38272753, 11881, 100, 66, 822, 28861, 77
Offset: 1

Views

Author

Robert G. Wilson v, Sep 15 2005

Keywords

Comments

First occurrence of 2n-1 in A110566.
Sequence continues: a(18)=?, 1332, 162, 2758521, 24649, 21, a(24)=?, 294, a(26)=?, 1166, 110, 126059, 201957, 3660, 37553041, 344929, 296341, a(35)=?, 25155299, a(37)=?, 500, 42

Crossrefs

Cf. A110566, A098464, A112813, A112814, A112815, A112816, A112817, A112818, A112819, A112820, A112821.

Programs

  • Mathematica
    a = h = 1; t = Table[0, {100}]; Do[a = LCM[a, n]; h = h + 1/n; b = a/Denominator[h]; If[b < 101 && t[[(b + 1)/2]] == 0, t[[(b + 1)/2]] = n], {n, 500000}]; t
  • Python
    from fractions import Fraction
from sympy import lcm
def A112822(n):
    k, l, h = 1, 1, Fraction(1,1)
    while l != h.denominator*(2*n-1):
        k += 1
        l = lcm(l,k)
        h += Fraction(1,k)
    return k # Chai Wah Wu, Mar 06 2021

Extensions

a(11), a(32) from Max Alekseyev, Nov 29 2013
a(33)-a(34) from Chai Wah Wu, Mar 06 2021
a(36), a(38), a(39) from Chai Wah Wu, Mar 12 2021

A112813 Numbers k such that lcm(1,2,3,...,k)/3 equals the denominator of the k-th harmonic number H(k).

Original entry on oeis.org

6, 7, 8, 18, 19, 25, 26, 54, 55, 56, 57, 58, 59, 60, 61, 62, 72, 73, 74, 75, 76, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231
Offset: 1

Views

Author

Robert G. Wilson v, Sep 17 2005

Keywords

Comments

When 3 occurs in A110566.

Links

Crossrefs

Cf. A002805, A003418, A110566.
Cf. A098464, A112814, A112815, A112816, A112817, A112818, A112819, A112820, A112821, A112822.

Programs

  • Mathematica
    f[n_] := LCM @@ Range[n]/Denominator[ HarmonicNumber[n]]; Select[ Range[231], f[ # ] == 3 &]
  • PARI
    isok(n) = lcm(vector(n, i, i)) == 3*denominator(sum(i=1, n, 1/i)); \\ Michel Marcus, Mar 07 2018

A112814 Numbers k such that lcm(1,2,3,...,k)/5 equals the denominator of the k-th harmonic number H(k).

Original entry on oeis.org

105, 106, 107, 108, 109, 2625, 2626, 2627, 2628, 2629, 2630, 2631, 2632, 2633, 2634, 2635, 2636, 2637, 2638, 2639, 2640, 2641, 2642, 2643, 2644, 2645, 2646, 2647, 2648, 2649, 2650, 2651, 2652, 2653, 2654, 2655, 2656, 2657, 2658, 2659, 2660, 2661, 2662
Offset: 1

Views

Author

Robert G. Wilson v, Sep 17 2005

Keywords

Comments

When 5 occurs in A110566.

Links

Crossrefs

Cf. A002805, A003418, A110566.
Cf. A098464, A112813, A112815, A112816, A112817, A112818, A112819, A112820, A112821, A112822.

Programs

  • Mathematica
    f[n_] := LCM @@ Range[n]/Denominator[ HarmonicNumber[n]]; Select[ Range[2662], f[ # ] == 5 &]
  • PARI
    isok(n) = lcm(vector(n, i, i)) == 5*denominator(sum(i=1, n, 1/i)); \\ Michel Marcus, Mar 07 2018

A112815 Numbers k such that lcm(1,2,3,...,k)/7 equals the denominator of the k-th harmonic number H(k).

Original entry on oeis.org

44, 45, 46, 47, 48, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 2209, 2210, 2211, 2212, 2213, 2214, 2215, 2216, 2217, 2218, 2219
Offset: 1

Views

Author

Robert G. Wilson v, Sep 17 2005

Keywords

Comments

When 7 occurs in A110566.

Links

Crossrefs

Cf. A002805, A003418, A110566.
Cf. A098464, A112813, A112814, A112816, A112817, A112818, A112819, A112820, A112821, A112822.

Programs

  • Mathematica
    f[n_] := LCM @@ Range[n]/Denominator[ HarmonicNumber[n]]; Select[ Range[2219], f[ # ] == 7 &]
  • PARI
    isok(n) = lcm(vector(n, i, i)) == 7*denominator(sum(i=1, n, 1/i)); \\ Michel Marcus, Mar 07 2018

A112816 Numbers k such that lcm(1,2,3,...,k)/9 equals the denominator of the k-th harmonic number H(k).

Original entry on oeis.org

63, 64, 65, 69, 70, 71, 189, 190, 191, 192, 193, 194, 195, 196, 197, 207, 208, 209, 210, 211, 212, 213, 214, 215, 1701, 1702, 1703, 1704, 1705, 1706, 1707, 1708, 1709, 1710, 1711, 1712, 1713, 1714, 1715, 1716, 1717, 1718, 1719, 1720, 1721, 1722, 1723, 1724
Offset: 1

Views

Author

Robert G. Wilson v, Sep 17 2005

Keywords

Comments

When 9 occurs in A110566.

Links

Crossrefs

Cf. A002805, A003418, A110566.
Cf. A098464, A112813, A112814, A112815, A112817, A112818, A112819, A112820, A112821, A112822.

Programs

  • Mathematica
    f[n_] := LCM @@ Range[n]/Denominator[ HarmonicNumber[n]]; Select[ Range[1724], f[ # ] == 9 &]

Extensions

Definition corrected by Jinyuan Wang, May 03 2020

A112817 Numbers k such that lcm(1,2,3,...,k)/11 equals the denominator of the k-th harmonic number H(k).

Original entry on oeis.org

33, 34, 35, 36, 37, 38, 39, 40, 41, 81, 82, 83, 84, 85, 86, 87, 363, 364, 365, 366, 367, 368, 369, 370, 371, 372, 373, 374, 375, 376, 406, 407, 408, 409, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 420, 421, 422, 423, 424, 425, 426, 427, 428, 429, 430
Offset: 1

Views

Author

Robert G. Wilson v, Sep 17 2005

Keywords

Comments

When 11 occurs in A110566.

Links

Crossrefs

Cf. A002805, A003418, A110566.
Cf. A098464, A112813, A112814, A112815, A112816, A112818, A112819, A112820, A112821, A112822.

Programs

  • Mathematica
    f[n_] := LCM @@ Range[n]/Denominator[ HarmonicNumber[n]]; Select[ Range[430], f[ # ] == 11 &]
Select[Range[450],1/11*LCM@@Range[#]==Denominator[HarmonicNumber[#]]&] (* Harvey P. Dale, Jan 06 2019 *)

Extensions

Name (definition) corrected by Harvey P. Dale, Jan 06 2019

A112818 Numbers k such that lcm(1,2,3,...,k)/13 equals the denominator of the k-th harmonic number H(k).

Original entry on oeis.org

156, 157, 158, 159, 160, 161, 27380, 27381, 27382, 27383, 27384, 27385, 27386, 27387, 27388, 27389, 27390, 27391, 27392, 27393, 27394, 27395, 27396, 27397, 27398, 27399, 27400, 27401, 27402, 27403, 27404, 27405, 27406, 27407, 27408
Offset: 1

Views

Author

Robert G. Wilson v, Sep 17 2005

Keywords

Comments

When 13 occurs in A110566.

Links

Crossrefs

Cf. A002805, A003418, A110566.
Cf. A098464, A112813, A112814, A112815, A112816, A112817, A112819, A112820, A112821, A112822.

Programs

Extensions

Definition corrected by Jinyuan Wang, May 03 2020

A112819 Numbers k such that lcm(1,2,3,...,k)/15 equals the denominator of the k-th harmonic number H(k).

Original entry on oeis.org

20, 24, 529, 530, 531, 532, 533, 534, 535, 536, 537, 538, 539, 540, 541, 542, 543, 544, 545, 546, 547, 548, 549, 550, 551, 552, 553, 554, 555, 556, 557, 558, 41889597, 41889598, 41889599, 41889600, 41889601, 41889602, 41889603, 41889604, 41889605, 41889606, 41889607
Offset: 1

Views

Author

Robert G. Wilson v, Sep 17 2005

Keywords

Comments

When 15 occurs in A110566.

Links

Crossrefs

Cf. A002805, A003418, A110566.
Cf. A098464, A112813, A112814, A112815, A112816, A112817, A112818, A112820, A112821, A112822.

Programs

  • Mathematica
    a = h = 1; t = {}; Do[a = LCM[a, n]; h = h + 1/n; If[a/Denominator[h] == 15, AppendTo[t, n]], {n, 10^6}]; t

Extensions

Definition corrected by Jinyuan Wang, May 03 2020
More terms from Chai Wah Wu, Mar 18 2021

A112820 Numbers k such that lcm(1,2,3,...,k)/17 equals the denominator of the k-th harmonic number H(k).

Original entry on oeis.org

272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 79507, 79508, 79509, 79510, 79511, 79512, 79513, 79514, 79515, 79516, 79517, 79518, 79519, 79520, 79521, 79522, 79523, 79524, 79525, 79526, 79527, 79528
Offset: 1

Views

Author

Robert G. Wilson v, Sep 17 2005

Keywords

Comments

When 17 occurs in A110566.

Links

Crossrefs

Cf. A002805, A003418, A110566.
Cf. A098464, A112813, A112814, A112815, A112816, A112817, A112818, A112819, A112821, A112822.

Programs

  • Mathematica
    a = h = 1; t = {}; Do[a = LCM[a, n]; h = h + 1/n; If[a/Denominator[h] == 17, AppendTo[t, n]], {n, 79528}]; t

Extensions

Definition corrected by Jinyuan Wang, May 03 2020

A342350 Numbers k such that lcm(1,2,3,...,k)/21 equals the denominator of the k-th harmonic number H(k).

Original entry on oeis.org

38272753, 38272754, 38272755, 38272756, 38272757, 38272758, 38272759, 38272760, 38272761, 38272762, 38272763, 38272764, 38272765, 38272766, 38272767, 38272768, 38272769, 38272770, 38272771, 38272772, 38272773, 38272774, 38272775, 38272776, 38272777, 38272778
Offset: 1

Views

Author

Chai Wah Wu, Mar 17 2021

Keywords

Comments

Positions where 21 occurs in A110566.

Links

Crossrefs

Cf. A002805, A003418, A110566.
Cf. A098464, A112813, A112814, A112815, A112816, A112817, A112818, A112819, A112820, A112821, A112822.
Showing 1-10 of 11 results. Next

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

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