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.

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A274281 Numbers that are a product of distinct Lucas numbers (2,1,3,4,7,11,...)

Original entry on oeis.org

1, 2, 3, 4, 6, 7, 8, 11, 12, 14, 18, 21, 22, 24, 28, 29, 33, 36, 42, 44, 47, 54, 56, 58, 66, 72, 76, 77, 84, 87, 88, 94, 108, 116, 123, 126, 132, 141, 144, 152, 154, 168, 174, 188, 198, 199, 203, 216, 228, 231, 232, 246, 252, 264, 282, 304, 308, 319, 322
Offset: 1

Views

Author

Clark Kimberling, Jun 17 2016

Keywords

Comments

See the Comment on distinct-product sequences in A160009.

Examples

			The Lucas numbers are 2,1,3,4,7,11,18,29,..., so that the sequence of all products of distinct Lucas numbers, in increasing order, are 1, 2, 3, 4, 6, 7, 8, 11, 12, 14, 18, 21, 22, 24, 28, 29,...

Links

Crossrefs

Cf. A160009, A274280.

Programs

  • Mathematica
    f[1] = 2; f[2] = 1; z = 32; f[n_] := f[n - 1] + f[n - 2]; f = Table[f[n], {n, 1, z}]; f
s = {1}; Do[s = Union[s, Select[s*f[[i]], # <= f[[z]] &]], {i, z}]; s

A274191 Numbers that are a product of distinct numbers in A022086.

Original entry on oeis.org

3, 6, 9, 15, 18, 24, 27, 39, 45, 54, 63, 72, 90, 102, 117, 135, 144, 162, 165, 189, 216, 234, 267, 270, 306, 351, 360, 378, 405, 432, 495, 567, 585, 612, 648, 699, 702, 801, 810, 918, 936, 945, 990, 1053, 1080, 1131, 1134, 1296, 1485, 1512, 1530, 1602, 1701
Offset: 1

Views

Author

Clark Kimberling, Jun 17 2016

Keywords

Comments

See the Comment on distinct-product sequences in A160009.

Examples

			17 = 3*6; 405 = 3*9*15.

Links

Crossrefs

Cf. A022086, A160009, A274288.

Programs

  • Mathematica
    f[1] = 3; f[2] = 6; z = 33; f[n_] := f[n - 1] + f[n - 2]; f = Table[f[n], {n, 1, z}]; f
s = {1}; Do[s = Union[s, Select[s*f[[i]], # <= f[[z]] &]], {i, z}]; s1 = Rest[s]

A274286 Numbers that are a product of distinct numbers in row 2 of the Wythoff array, A035513.

Original entry on oeis.org

4, 7, 11, 18, 28, 29, 44, 47, 72, 76, 77, 116, 123, 126, 188, 198, 199, 203, 304, 308, 319, 322, 329, 492, 504, 517, 521, 522, 532, 792, 796, 812, 836, 843, 846, 861, 1276, 1288, 1316, 1353, 1363, 1364, 1368, 1386, 1393, 2068, 2084, 2088, 2128, 2189, 2204
Offset: 1

Views

Author

Clark Kimberling, Jun 17 2016

Keywords

Comments

See the Comment on distinct-product sequences in A160009.

Examples

			28 = 4*7, 308 = 4*7*11.

Links

Crossrefs

Cf. A160009, A274280.

Programs

  • Mathematica
    f[1] = 4; f[2] = 7; z = 33; f[n_] := f[n - 1] + f[n - 2]; f = Table[f[n], {n, 1, z}]; f
s = {1}; Do[s = Union[s, Select[s*f[[i]], # <= f[[z]] &]], {i, z}]; s1 = Rest[s]

A274287 Numbers that are a product of distinct numbers in row 3 of the Wythoff array, A035513.

Original entry on oeis.org

6, 10, 16, 26, 42, 60, 68, 96, 110, 156, 160, 178, 252, 260, 288, 408, 416, 420, 466, 660, 672, 680, 754, 960, 1068, 1088, 1092, 1100, 1220, 1560, 1728, 1760, 1768, 1780, 1974, 2496, 2520, 2796, 2848, 2856, 2860, 2880, 3194, 4032, 4080, 4160, 4524, 4608
Offset: 1

Views

Author

Clark Kimberling, Jun 17 2016

Keywords

Comments

See the Comment on distinct-product sequences in A160009.

Examples

			60 = 6*10, 960 = 6*10*16.

Links

Crossrefs

Cf. A160009.

Programs

  • Mathematica
    f[1] = 6; f[2] = 10; z = 33; f[n_] := f[n - 1] + f[n - 2]; f = Table[f[n], {n, 1, z}]; f
s = {1}; Do[s = Union[s, Select[s*f[[i]], # <= f[[z]] &]], {i, z}]; Rest[s]

A274283 Numbers that are a product of distinct numbers in A022095.

Original entry on oeis.org

1, 5, 6, 11, 17, 28, 30, 45, 55, 66, 73, 85, 102, 118, 140, 168, 187, 191, 225, 270, 308, 309, 330, 365, 438, 476, 495, 500, 510, 590, 708, 765, 803, 809, 840, 935, 955, 1122, 1146, 1241, 1260, 1298, 1309, 1350, 1540, 1545, 1848, 1854, 2006, 2044, 2101, 2118
Offset: 1

Views

Author

Clark Kimberling, Jun 17 2016

Keywords

Comments

See the Comment on distinct-product sequences in A160009.

Examples

			30 = 5*6, 330 = 5*6*11.

Links

Crossrefs

Cf. A160009.

Programs

  • Mathematica
    f[1] = 1; f[2] = 5; z = 32; f[n_] := f[n - 1] + f[n - 2]; f = Table[f[n], {n, 1, z}]; f
s = {1}; Do[s = Union[s, Select[s*f[[i]], # <= f[[z]] &]], {i, z}]; s

A274284 Numbers that are a product of distinct numbers in A006355.

Original entry on oeis.org

2, 4, 6, 8, 10, 12, 16, 20, 24, 26, 32, 40, 42, 48, 52, 60, 64, 68, 80, 84, 96, 104, 110, 120, 128, 136, 156, 160, 168, 178, 192, 208, 220, 240, 252, 260, 272, 288, 312, 320, 336, 356, 384, 408, 416, 420, 440, 466, 480, 504, 520, 544, 576, 624, 640, 660, 672
Offset: 1

Views

Author

Clark Kimberling, Jun 17 2016

Keywords

Comments

See the Comment on distinct-product sequences in A160009.

Examples

			8 = 2*4, 480 = 2*4*6*10.

Links

Crossrefs

Cf. A160009.

Programs

  • Mathematica
    f[1] = 2; f[2] = 4; z = 32; f[n_] := f[n - 1] + f[n - 2]; f = Table[f[n], {n, 1, z}]; f
s = {2}; Do[s = Union[s, Select[s*f[[i]], # <= f[[z]] &]], {i, z}]; s

A274285 Numbers that are a product of distinct numbers in A013655.

Original entry on oeis.org

2, 5, 7, 10, 12, 14, 19, 24, 31, 35, 38, 50, 60, 62, 70, 81, 84, 95, 100, 120, 131, 133, 155, 162, 168, 190, 212, 217, 228, 250, 262, 266, 310, 343, 350, 372, 405, 420, 424, 434, 456, 500, 555, 567, 589, 600, 655, 665, 686, 700, 744, 810, 840, 898, 917, 950
Offset: 1

Views

Author

Clark Kimberling, Jun 17 2016

Keywords

Comments

See the Comment on distinct-product sequences in A160009.

Examples

			10 = 2*5, 120 = 2*5*12.

Links

Crossrefs

Cf. A160009.

Programs

  • Mathematica
    f[1] = 2; f[2] = 5; z = 33; f[n_] := f[n - 1] + f[n - 2]; f = Table[f[n], {n, 1, z}]; f
s = {1}; Do[s = Union[s, Select[s*f[[i]], # <= f[[z]] &]], {i, z}]; s1 = Rest[s]

A274353 Number of factors L(i) > 1 of A274280(n), where L = A000032 (Lucas numbers, 1,3,4,...)

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 3, 2, 2, 1, 2, 3, 2, 2, 2, 1, 2, 3, 2, 3, 2, 3, 2, 1, 2, 3, 2, 3, 2, 3, 2, 1, 2, 2, 3, 3, 2, 3, 3, 2, 3, 2, 1, 2, 2, 3, 4, 3, 2, 3, 3, 2, 3, 2, 2, 1, 2, 3, 2, 3, 4, 3, 2, 3, 3, 3, 2, 3, 3, 2, 2, 1, 2, 3, 2
Offset: 1

Views

Author

Clark Kimberling, Jun 18 2016

Keywords

Examples

			The products of distinct Lucas numbers, arranged in increasing order, comprise A274280.  The list begins with 1, 3, 4, 7, 11, 12 = 3*4, so that a(6) = 2.

Links

Crossrefs

Cf. A000032, A274280, A274347, A274348, A160009, A272947, A274354.

Programs

  • Mathematica
    r[1] := 1; r[2] := 3; r[n_] := r[n] = r[n - 1] + r[n - 2];
s = {1}; z = 40; f = Map[r, Range[z]]; Take[f, 10]
Do[s = Union[s, Select[s*f[[i]], # <= f[[z]] &]], {i, z}];
infQ[n_] := MemberQ[f, n];
a = Table[#[[Flatten[Position[Map[Apply[Times, #] &, #], s[[n]]]][[1]]]] &[
Rest[Subsets[Map[#[[1]] &, Select[Map[{#, infQ[#]} &,
Divisors[s[[n]]]], #[[2]] && #[[1]] > 1 &]]]]], {n, 2, 200}];
ans = Join[{{1}}, a]; Take[ans, 8]
w = Map[Length, ans] (* A274353 *)
Map[Apply[Times, #] &, Select[ans, Length[#] == 2 &]] (* A274347 *)
Map[Apply[Times, #] &, Select[ans, Length[#] == 3 &]] (* A274348 *)
(* Peter J. C. Moses, Jun 17 2016 *)

A274452 Products of distinct Narayana's cow numbers (A000930).

Original entry on oeis.org

2, 3, 4, 6, 8, 9, 12, 13, 18, 19, 24, 26, 27, 28, 36, 38, 39, 41, 48, 52, 54, 56, 57, 60, 72, 76, 78, 82, 84, 88, 104, 108, 112, 114, 117, 120, 123, 129, 144, 152, 156, 162, 164, 168, 171, 176, 180, 189, 216, 224, 228, 234, 240, 246, 247, 252, 258, 264, 277
Offset: 1

Views

Author

Clark Kimberling, Jun 23 2016

Keywords

Examples

			The Narayana's cow numbers numbers are 1, 2, 3, 4, 6, 9, 13, 19, 28, ..., so that the sequence of all products of distinct members, in increasing order, is (2, 3, 4, 6, 8, 9, 12, 13, 18, 19, 24, ...).

Links

Crossrefs

Cf. A160009, A274280, A274432.

Programs

  • Mathematica
    r[1] := 1; r[2] := 1; r[3] = 1; r[n_] := r[n] = r[n - 1] + r[n - 3]
s = {1}; z = 60; f = Map[r, Range[z]]; Take[f, 20] (*A000930*)
Do[s = Union[s, Select[s*f[[i]], # <= f[[z]] &]], {i, z}];
Take[s, 2 z] (* A274452 *)

A274282 Numbers that are a product of distinct numbers in A000285.

Original entry on oeis.org

1, 4, 5, 9, 14, 20, 23, 36, 37, 45, 56, 60, 70, 92, 97, 115, 126, 148, 157, 180, 185, 207, 240, 254, 280, 300, 322, 333, 388, 411, 460, 485, 504, 518, 540, 628, 630, 665, 740, 785, 828, 840, 851, 873, 1016, 1035, 1076, 1200, 1270, 1288, 1332, 1358, 1380
Offset: 1

Views

Author

Clark Kimberling, Jun 17 2016

Keywords

Comments

See the Comment on distinct-product sequences in A160009.

Examples

			20 = 4*5, 180 = 4*5*9.

Crossrefs

Cf. A000285, A160009, A274288.

Programs

  • Mathematica
    f[1] = 1; f[2] = 4; z = 32; f[n_] := f[n - 1] + f[n - 2]; f = Table[f[n], {n, 1, z}]; f
s = {1}; Do[s = Union[s, Select[s*f[[i]], # <= f[[z]] &]], {i, z}]; s
Previous Showing 11-20 of 26 results. Next

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