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.

A088381 Numbers greater than the cube of their smallest prime factor.

Original entry on oeis.org

10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 33, 34, 36, 38, 39, 40, 42, 44, 45, 46, 48, 50, 51, 52, 54, 56, 57, 58, 60, 62, 63, 64, 66, 68, 69, 70, 72, 74, 75, 76, 78, 80, 81, 82, 84, 86, 87, 88, 90, 92, 93, 94, 96, 98, 99, 100, 102, 104, 105, 106, 108, 110, 111, 112
Offset: 1

Views

Author

Reinhard Zumkeller, Sep 28 2003

Keywords

Comments

a(n) > A020639(a(n))^3 = A088378(a(n)); complement of A088380;
a(n) > A088380(k) for n <= 28, a(n) < A088380(k) for n > 28.

Links

Crossrefs

Cf. A080257, A088378, A088380, A088383.
Cf. A020639, A138511 (subsequence).
Positions of numbers greater than 3 in A307908.

Programs

  • Haskell
    a088381 n = a088381_list !! (n-1)
a088381_list = filter f [1..] where
                      f x = p ^ 2 < div x p  where p = a020639 x
-- Reinhard Zumkeller, Jan 08 2015
  • Maple
    filter:= n -> n > min(numtheory:-factorset(n))^3:
select(filter, [$2..200]); # Robert Israel, Aug 11 2020
  • PARI
    isok(n) = n > factor(n)[1,1]^3; \\ Michel Marcus, Jan 08 2015

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

A088379 a(n) = (smallest prime factor of n)^4; a(1) = 1.

Original entry on oeis.org

1, 16, 81, 16, 625, 16, 2401, 16, 81, 16, 14641, 16, 28561, 16, 81, 16, 83521, 16, 130321, 16, 81, 16, 279841, 16, 625, 16, 81, 16, 707281, 16, 923521, 16, 81, 16, 625, 16, 1874161, 16, 81, 16, 2825761, 16, 3418801, 16, 81, 16, 4879681, 16, 2401, 16
Offset: 1

Views

Author

Reinhard Zumkeller, Sep 28 2003

Keywords

Links

Crossrefs

Cf. A020639, A000583, A088377, A088378.

Programs

  • Mathematica
    a[n_] := FactorInteger[n][[1, 1]]^4; Array[a, 100] (* Amiram Eldar, May 16 2025 *)
  • PARI
    a(n) = if(n == 1, 1, factor(n)[1,1]^4); \\ Amiram Eldar, May 16 2025

Formula

a(n) = A000583(A020639(n)).
a(n) = A088377(n)^2. - Amiram Eldar, May 16 2025

A088380 Numbers not exceeding the cube of their smallest prime factor.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 35, 37, 41, 43, 47, 49, 53, 55, 59, 61, 65, 67, 71, 73, 77, 79, 83, 85, 89, 91, 95, 97, 101, 103, 107, 109, 113, 115, 119, 121, 125, 127, 131, 133, 137, 139, 143, 149, 151, 157, 161, 163, 167, 169
Offset: 1

Views

Author

Reinhard Zumkeller, Sep 28 2003

Keywords

Comments

a(n) <= A020639(a(n))^3 = A088378(a(n)); complement of A088381;
a(n) < A088381(k) for n <= 28, a(n) > A088381(k) for n > 28.

Links

Crossrefs

Cf. A000430, A088382, A020639, A088378, A088381.
Positions of numbers less than 4 in A307908.

Programs

  • Haskell
    a088380 n = a088382_list !! (n-1)
a088380_list = [x | x <- [1..], x <= a020639 x ^ 3]
-- Reinhard Zumkeller, Feb 06 2015
  • Mathematica
    Select[Range[200],#<=FactorInteger[#][[1,1]]^3&] (* Harvey P. Dale, Apr 28 2022 *)
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.