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.

A378160 The number of distinct prime factors of !n = A000166(n).

Original entry on oeis.org

0, 1, 1, 2, 2, 3, 3, 4, 2, 3, 2, 4, 3, 3, 4, 3, 3, 4, 5, 5, 4, 7, 5, 6, 4, 5, 7, 6, 6, 7, 4, 4, 4, 8, 4, 6, 4, 5, 6, 6, 4, 7, 2, 4, 7, 8, 6, 5, 7, 6, 7, 7, 4, 6, 9, 6, 6, 6, 6, 6, 4, 4, 5, 4, 3, 6, 6, 6, 6, 6, 7, 7, 4, 8, 6, 5, 8, 6, 4, 4, 5, 8, 4, 7, 7, 8, 6
Offset: 2

Views

Author

Amiram Eldar, Nov 18 2024

Keywords

Links

Crossrefs

Cf. A000166, A001221, A152024, A195207, A195208, A195209, A195210, A301423, A378157, A378161, A378162.

Programs

  • Mathematica
    Array[PrimeNu[Subfactorial[#]] &, 40, 2]
  • PARI
    lista(nmax) = {my(s = 0); for(n = 2, nmax, s = n * s + (-1)^n; print1(omega(s), ", "));}

Formula

a(n) = A001221(A000166(n)).
a(n) >= A001221(n-1) + 1 for n >=5.

Extensions

a(82)-a(88) from Jinyuan Wang, Nov 24 2024

A378161 The number of prime factors of !n = A000166(n), counted with multiplicity.

Original entry on oeis.org

0, 1, 2, 3, 2, 4, 3, 6, 5, 3, 3, 6, 3, 3, 5, 6, 3, 8, 5, 6, 5, 8, 5, 9, 5, 5, 11, 7, 6, 9, 4, 8, 6, 8, 4, 10, 5, 5, 7, 8, 4, 8, 2, 7, 12, 8, 6, 9, 8, 7, 8, 8, 4, 10, 10, 8, 7, 6, 6, 8, 4, 4, 8, 9, 3, 8, 6, 7, 7, 6, 7, 13, 4, 8, 8, 6, 9, 7, 4, 7, 10, 8, 4, 9, 7
Offset: 2

Views

Author

Amiram Eldar, Nov 18 2024

Keywords

Links

Crossrefs

Cf. A001222, A000166, A152024, A195207, A195208, A195209, A195210, A301423, A378157, A378160, A378162.

Programs

  • Mathematica
    Array[PrimeOmega[Subfactorial[#]] &, 40, 2]
  • PARI
    lista(nmax) = {my(s = 0); for(n = 2, nmax, s = n * s + (-1)^n; print1(bigomega(s), ", "));}

Formula

a(n) = A001222(A000166(n)).
a(n) >= A001222(n-1) + 1 for n >=4, with equality if and only if n is in A301423.

Extensions

a(82)-a(86) from Jinyuan Wang, Nov 24 2024

A378159 The least prime dividing A000255(n); a(1) = 1.

Original entry on oeis.org

1, 3, 11, 53, 3, 13, 11, 3, 1468457, 11, 3, 1373, 34361893981, 3, 17713, 2130617, 3, 11, 13, 3, 11, 617, 3, 37, 11, 3, 179, 14633, 3, 76463, 97, 3, 337, 1049, 3, 11, 7237598635049, 3, 67, 11, 3, 22742406079421034331584846001936724930824184898296683, 11, 3, 13
Offset: 1

Views

Author

Amiram Eldar, Nov 18 2024

Keywords

Links

Crossrefs

Cf. A000255, A020639, A301423, A378157.

Programs

  • Mathematica
    FactorInteger[#][[1, 1]] & /@ Table[Subfactorial[n + 2]/(n + 1), {n, 1, 44}]
  • PARI
    lpf(n) = if(n == 1, 1, factor(n)[1,1]);
lista(nmax) = {my(s = 1); for(n = 1, nmax, s = (n * (n+2) * s + (-1)^n)/(n+1); print1(lpf(s), ", "));}

Formula

a(n) = A020639(A000255(n)).
a(n) = A000255(n) if and only if n+2 is a term of A301423.
a(3*n-1) = 3.
Showing 1-3 of 3 results.

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

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