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 1-3 of 3 results.

A241793 Least number k such that k^n and k^n-1 contain the same number of prime factors (counted with multiplicity) or 0 if no such k exists.

Original entry on oeis.org

3, 34, 5, 15, 17, 55, 79, 5, 53, 23, 337, 13, 601, 79, 241, 41, 18433, 31, 40961, 89, 3313, 1153
Offset: 1

Views

Author

Derek Orr, May 23 2014

Keywords

Comments

a(23) > 3250.
a(24) = 79. - Jacques Tramu, Sep 16 2018
100000 < a(23) <= 286721. - Jon E. Schoenfield, Sep 25 2018

Examples

			2^1 (2) and 2^1-1 (1) do not have the same number of prime factors. 3^1 (3) and 3^1-1 (2) have the same number of prime factors. Thus a(1) = 3.
		

Crossrefs

Cf. A001222 (bigomega), A242786.

Programs

  • PARI
    a(n)=for(k=2,oo,if(bigomega(k^n)==bigomega(k^n-1),return(k)));

Extensions

a(17) and a(19) corrected by Jacques Tramu, Sep 16 2018

A368162 a(n) is the smallest number k > 0 such that bigomega(k^n + 1) = n.

Original entry on oeis.org

1, 3, 3, 43, 7, 32, 23, 643, 17, 207, 251, 3255, 255, 1568, 107
Offset: 1

Views

Author

Daniel Suteu, Dec 14 2023

Keywords

Comments

a(16) <= 206874667; a(17) = 4095; a(18) = 6272; a(21) = 1151.

Examples

			a(5) = 7 is the smallest number of the set {k(i)} = {7, 14, 24, 26, 46, 51, ...} where k(i)^5 + 1 has exactly 5 prime factors counted with multiplicity.
		

Crossrefs

Programs

  • PARI
    a(n) = my(k=1); while (bigomega(k^n+1) != n, k++); k;

A379768 a(n) is the smallest prime p such that omega(p^n + 1) = n.

Original entry on oeis.org

2, 3, 5, 43, 17, 47, 151, 1697, 59, 2153, 521, 13183, 30089, 66569, 761
Offset: 1

Views

Author

Daniel Suteu, Jan 06 2025

Keywords

Comments

2*10^6 < a(16) <= 206874667; a(18) = 33577; a(20) <= 3258569.
A219018(n) <= a(n) <= A280005(n).

Examples

			a(3) = 5 is the smallest prime of the set {p(i)} = {5, 11, 13, 19, 23, ...} where omega(p(i)^3 + 1) = 3.
		

Crossrefs

Programs

  • Mathematica
    a[n_] := Module[{p = 2}, While[PrimeNu[p^n + 1] != n, p = NextPrime[p]]; p]; Print[Array[a, 11]]
  • PARI
    a(n) = forprime(p=2, oo, if(omega(p^n+1) == n, return(p)));
Showing 1-3 of 3 results.