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 1-5 of 5 results.

A000093 a(n) = floor(n^(3/2)).

Original entry on oeis.org

0, 1, 2, 5, 8, 11, 14, 18, 22, 27, 31, 36, 41, 46, 52, 58, 64, 70, 76, 82, 89, 96, 103, 110, 117, 125, 132, 140, 148, 156, 164, 172, 181, 189, 198, 207, 216, 225, 234, 243, 252, 262, 272, 281, 291, 301, 311, 322, 332, 343, 353, 364, 374, 385, 396, 407, 419, 430
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

References

  • B. K. Agarwala and F. C. Auluck, Statistical mechanics and partitions into non-integral powers of integers, Proc. Camb. Phil. Soc., 47 (1951), 207-216.
  • N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

Integer part of square root of n^k: A000196 (k=1), this sequence (k=3), A155013 (k=5), A155014 (k=7), A155015 (k=11), A155016 (k=13), A155018 (k=15), A155019 (k=17).
Cf. A002821.
Cf. A185549.

Programs

  • Haskell
    a000093 = a000196 . a000578  -- Reinhard Zumkeller, Jul 11 2014
  • Maple
    Digits := 100: A000093 := n->floor(evalf(n^(3/2)));
  • Mathematica
    Table[ Floor[ Sqrt[n^3]], {n, 0, 60}]
  • PARI
    a(n)=if(n<0,0,sqrtint(n^3))
  • Python
    from math import isqrt
def A000093(n): return isqrt(n**3) # Chai Wah Wu, Sep 08 2024

Formula

a(n) = A077121(n) - 1. [Reinhard Zumkeller, Oct 31 2009]
a(n) = floor(n*sqrt(n)). [Arkadiusz Wesolowski, Jun 01 2011]
a(n) = A000196(A000578(n)) = A074704(n)+n*A000196(n). [Reinhard Zumkeller, Jun 27 2011]

Extensions

More terms from James Sellers, May 04 2000

A155013 Integer part of square root of n^5 = A000584(n).

Original entry on oeis.org

1, 5, 15, 32, 55, 88, 129, 181, 243, 316, 401, 498, 609, 733, 871, 1024, 1191, 1374, 1573, 1788, 2020, 2270, 2536, 2821, 3125, 3446, 3787, 4148, 4528, 4929, 5350, 5792, 6255, 6740, 7247, 7776, 8327, 8901, 9498, 10119, 10763, 11432, 12124, 12841, 13584, 14351
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jan 19 2009

Keywords

Links

Crossrefs

Cf. A000093.
Integer part of square root of n^k: A000196 (k=1), A000093 (k=3), this sequence (k=5), A155014 (k=7), A155015 (k=11), A155016 (k=13), A155018 (k=15), A155019 (k=17),

Programs

  • Magma
    [Floor(Sqrt(n^5)): n in [1..30]]; // G. C. Greubel, Dec 30 2017
  • Mathematica
    a={};Do[AppendTo[a,IntegerPart[(n^5)^(1/2)]],{n,5!}];a
IntegerPart[Sqrt[Range[50]^5]] (* Harvey P. Dale, May 14 2012 *)
Table[Floor[Sqrt[n^5]], {n,1,30}] (* G. C. Greubel, Dec 30 2017 *)
  • PARI
    for(n=1,30, print1(sqrtint(n^5), ", ")) \\ G. C. Greubel, Dec 30 2017
  • Python
    from math import isqrt
def A155013(n): return isqrt(n**5) # Chai Wah Wu, Aug 08 2025

Formula

a(n) = floor(n^2 * sqrt(n)). - Davide Rotondo, Dec 01 2024

A155018 Integer part of square root of n^15 = A010803(n).

Original entry on oeis.org

0, 1, 181, 3787, 32768, 174692, 685700, 2178889, 5931641, 14348907, 31622776, 64631634, 124125023, 226242995, 394421215, 661735513, 1073741824, 1691869691, 2597429617, 3896296578, 5724334022, 8253624572, 11699575548, 16328969210
Offset: 0

Views

Author

Vladimir Joseph Stephan Orlovsky, Jan 19 2009

Keywords

Links

Crossrefs

Integer part of square root of n^k: A000196 (k=1), A000093 (k=3), A155013 (k=5), A155014 (k=7), A155015 (k=11), A155016 (k=13), this sequence (k=15), A155019 (k=17).

Programs

  • Magma
    [Floor(Sqrt(n^15)): n in [1..30]]; // G. C. Greubel, Dec 30 2017
  • Mathematica
    a={};Do[AppendTo[a,IntegerPart[(n^15)^(1/2)]],{n,0,5!}];a
Table[Floor[Sqrt[n^15]], {n,1,30}] (* G. C. Greubel, Dec 30 2017 *)
  • PARI
    for(n=1,30, print1(floor(sqrt(n^15)), ", ")) \\ G. C. Greubel, Dec 30 2017

Extensions

Offset corrected by Alois P. Heinz, Sep 27 2014

A155019 Integer part of square root of n^17 = A010805(n).

Original entry on oeis.org

0, 1, 362, 11363, 131072, 873464, 4114202, 15252229, 47453132, 129140163, 316227766, 710947978, 1489500287, 2941158941, 5521897022, 9926032708, 17179869184, 28761784747, 46753733110, 74029634996, 114486680447
Offset: 0

Views

Author

Vladimir Joseph Stephan Orlovsky, Jan 19 2009

Keywords

Links

Crossrefs

Integer part of square root of n^k: A000196 (k=1), A000093 (k=3), A155013 (k=5), A155014 (k=7), A155015 (k=11), A155016 (k=13), A155018 (k=15), this sequence (k=17).

Programs

  • Magma
    [Floor(Sqrt(n^17)): n in [0..30]]; // G. C. Greubel, Dec 30 2017
  • Mathematica
    a={};Do[AppendTo[a,IntegerPart[(n^17)^(1/2)]],{n,0,5!}];a
Table[Floor[Sqrt[n^17]], {n,0,30}] (* G. C. Greubel, Dec 30 2017 *)
  • PARI
    for(n=0,30, print1(floor(sqrt(n^17)), ", ")) \\ G. C. Greubel, Dec 30 2017

Extensions

Offset corrected by Alois P. Heinz, Sep 27 2014

A238170 Integer part of square root of A001017: a(n) = floor(n^(9/2)).

Original entry on oeis.org

0, 1, 22, 140, 512, 1397, 3174, 6352, 11585, 19683, 31622, 48558, 71831, 102978, 143739, 196069, 262144, 344365, 445375, 568056, 715541, 891223, 1098758, 1342070, 1625363, 1953125, 2330129, 2761448, 3252453, 3808824, 4436552, 5141947, 5931641, 6812597, 7792110
Offset: 0

Views

Author

Philippe Deléham, Feb 21 2014

Keywords

Links

Crossrefs

Integer part of square root of n^k: A000196 (k=1), A000093 (k=3), A155013 (k=5), A155014 (k=7), this sequence (k=9), A155015 (k=11), A155016 (k=13), A155018 (k=15), A155019 (k=17).

Programs

  • Magma
    [Floor(n^(9/2)): n in [0..40]]; // Vincenzo Librandi, Feb 23 2014
  • Mathematica
    Table[Floor[n^(9/2)], {n,0,30}] (* G. C. Greubel, Dec 30 2017 *)
  • PARI
    a(n) = floor(n^(9/2)); \\ Joerg Arndt, Feb 23 2014
  • Python
    from math import isqrt
def A238170(n): return isqrt(n**9) # Chai Wah Wu, Jan 27 2023

Formula

a(n) = floor(n^(9/2)).
a(n) = A000196(A001017(n)).
a(n) = floor(n^4*sqrt(n)).
Showing 1-5 of 5 results.

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

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