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 1-4 of 4 results.

A088377 a(n) = (smallest prime factor of n)^2; a(1) = 1.

Original entry on oeis.org

1, 4, 9, 4, 25, 4, 49, 4, 9, 4, 121, 4, 169, 4, 9, 4, 289, 4, 361, 4, 9, 4, 529, 4, 25, 4, 9, 4, 841, 4, 961, 4, 9, 4, 25, 4, 1369, 4, 9, 4, 1681, 4, 1849, 4, 9, 4, 2209, 4, 49, 4, 9, 4, 2809, 4, 25, 4, 9, 4, 3481, 4, 3721, 4, 9, 4, 25, 4, 4489, 4, 9, 4, 5041, 4, 5329, 4, 9, 4
Offset: 1

Views

Author

Reinhard Zumkeller, Sep 28 2003

Keywords

Links

Crossrefs

Cf. A000290, A068319, A088378, A088379, A247180.

Programs

  • Mathematica
    a[n_] := FactorInteger[n][[1, 1]]^2; Array[a, 100] (* Amiram Eldar, May 16 2025 *)
  • PARI
    a(n) = if(n == 1, 1, factor(n)[1,1]^2); \\ Amiram Eldar, May 16 2025

Formula

a(n) = A000290(A020639(n)).
a(n) = sqrt(A088379(n)). - Amiram Eldar, May 16 2025

A088378 a(n) = (smallest prime factor of n)^3; a(1) = 1.

Original entry on oeis.org

1, 8, 27, 8, 125, 8, 343, 8, 27, 8, 1331, 8, 2197, 8, 27, 8, 4913, 8, 6859, 8, 27, 8, 12167, 8, 125, 8, 27, 8, 24389, 8, 29791, 8, 27, 8, 125, 8, 50653, 8, 27, 8, 68921, 8, 79507, 8, 27, 8, 103823, 8, 343, 8, 27, 8, 148877, 8, 125, 8, 27, 8, 205379, 8, 226981
Offset: 1

Views

Author

Reinhard Zumkeller, Sep 28 2003

Keywords

Links

Crossrefs

Cf. A020639, A000578, A088377, A088379.

Programs

  • Mathematica
    Table[FactorInteger[n][[1,1]]^3,{n,70}] (* Harvey P. Dale, Aug 05 2019 *)
  • PARI
    a(n) = if(n == 1, 1, factor(n)[1,1]^3); \\ Amiram Eldar, May 16 2025

Formula

a(n) = A000578(A020639(n)).

A088382 Numbers not exceeding the 4th power of their smallest prime factor.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 89, 91, 95, 97, 101, 103, 107, 109, 113, 115, 119, 121, 125, 127, 131, 133
Offset: 1

Views

Author

Reinhard Zumkeller, Sep 28 2003

Keywords

Comments

a(n) <= A020639(a(n))^4 = A088379(a(n)); complement of A088383;
a(n) < A088383(k) for n <= 67, a(n) > A088383(k) for n > 67.

Links

Crossrefs

Cf. A088380, A000430, A020639, A088379, A088383.
Positions of numbers less than 5 in A307908.

Programs

  • Haskell
    a088382 n = a088382_list !! (n-1)
a088382_list = [x | x <- [1..], x <= a020639 x ^ 4]
-- Reinhard Zumkeller, Feb 06 2015
  • Mathematica
    Select[Range[200],#<=FactorInteger[#][[1,1]]^4&] (* Harvey P. Dale, Jan 25 2015 *)

A088383 Numbers greater than the 4th power of their smallest prime factor.

Original entry on oeis.org

18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 87, 88, 90, 92, 93, 94, 96, 98, 99, 100, 102, 104, 105, 106, 108, 110, 111, 112, 114, 116, 117, 118, 120, 122, 123, 124, 126
Offset: 1

Views

Author

Reinhard Zumkeller, Sep 28 2003

Keywords

Comments

a(n) > A020639(a(n))^4 = A088379(a(n)); complement of A088382.
a(n) > A088382(k) for n <= 67, a(n) < A088382(k) for n > 67.

Links

Crossrefs

Cf. A088381, A080257, A020639, A088379, A088382.
Positions of numbers greater than 4 in A307908.

Programs

  • Haskell
    a088383 n = a088383_list !! (n-1)
a088383_list = [x | x <- [1..], x  a020639 x ^ 4]
-- Reinhard Zumkeller, Feb 06 2015
  • Mathematica
    Select[Range[200],#>(FactorInteger[#][[1,1]])^4&] (* Harvey P. Dale, Aug 15 2015 *)
Showing 1-4 of 4 results.

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

Content is available under The OEIS End-User License Agreement.