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 1-2 of 2 results.

A377844 Numbers that have a single odd exponent larger than 1 in their prime factorization.

Original entry on oeis.org

8, 24, 27, 32, 40, 54, 56, 72, 88, 96, 104, 108, 120, 125, 128, 135, 136, 152, 160, 168, 184, 189, 200, 224, 232, 243, 248, 250, 264, 270, 280, 288, 296, 297, 312, 328, 343, 344, 351, 352, 360, 375, 376, 378, 384, 392, 408, 416, 424, 432, 440, 456, 459, 472, 480, 486, 488, 500
Offset: 1

Views

Author

Amiram Eldar, Nov 09 2024

Keywords

Comments

First differs from A295661, A325990 and A376142 at n = 24: A295661(24) = A325990(24) = A376142(24) = 216 = 2^3 * 3^3 is not a term of this sequence.
Differs from A060476 by having the terms 432, 648, 1728, ..., and not having the terms 1, 216, 256, 768, 864, ... .
The asymptotic density of this sequence is Product_{p prime} (1 - 1/(p^2*(p+1))) * Sum_{p prime} (1/(p^3+p^2-1)) = 0.11498368544519741081... .

Crossrefs

Subsequence of A295661.
Subsequences: A065036, A143610, A163569.

Programs

  • Mathematica
    q[n_] := Count[FactorInteger[n][[;; , 2]], _?(# > 1 && OddQ[#] &)] == 1; Select[Range[500], q]
  • PARI
    is(k) = #select(x -> x>1 && x%2, factor(k)[, 2]) == 1;

A384442 Smallest k such that A361373(k) = n.

Original entry on oeis.org

1, 2, 4, 6, 10, 12, 18, 40, 36, 30, 60, 102, 84, 132, 150, 264, 210, 540, 330, 420, 660, 630, 840, 1050, 2100, 2340, 2520, 3150, 2310, 2730, 4290, 4620, 6930, 9240, 15960, 16170, 17850, 18480, 20790, 34650, 62370, 68250, 30030, 62790, 60060, 78540, 90090, 117810
Offset: 0

Views

Author

Michael De Vlieger, Jun 12 2025

Keywords

Comments

For n > 1, a(n) is composite, since A361373(p) = 1 for prime p.
For n = 0..2, a(n) = 2^n. For n > 2, a(n) is in A024619.

Examples

			Table of n, a(n) for n = 1..12, showing row a(n) of A377485.
          log n/log p
 n  a(n)  p_1 p_2 p_3  row n of A377485
-------------------------------------------------------------------------
 1:   2   1            {p}
 2:   4   2            {p, p^2}
 3:   6   2   1        {p, q, p^2}
 4:  10   3   1        {p, p^2, q, p^3}
 5:  12   3   2        {p, q, p^2, p^3, q^2}
 6:  18   4   2        {p, q, p^2, p^3, q^2, p^4}
 7:  40   5   2        {p, p^2, q, p^3, p^4, q^2, p^5}
 8:  36   5   3        {p, q, p^2, p^3, q^2, p^4, q^3, p^5}
 9:  30   4   3   2    {p, q, p^2, r, p^3, q^2, p^4, r^2, q^3}
10:  60   5   3   2    {p, q, p^2, r, p^3, q^2, p^4, r^2, q^3, p^5}
11: 102   6   4   1    {p, q, p^2, p^3, q^2, p^4, r, q^3, p^5, p^6, q^4}
12:  84   6   4   2    {p, q, p^2, r, p^3, q^2, p^4, q^3, p^5, r^2, p^6, q^4}
		

Crossrefs

Programs

  • Mathematica
    nn = 30030; t[_] := 0; u = 1; Do[(If[t[#] == 0, t[#] = n]; If[# == u, While[t[u] != 0, u++]]) &[Total@ Map[Floor@ Log[#, n] &, FactorInteger[n][[All, 1]] ] ], {n, 2, nn}]; {1}~Join~Array[t, u - 1]
Showing 1-2 of 2 results.