A378160 -id:A378160 - cp's OEIS frontend

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

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

Amiram Eldar, Nov 18 2024

nonn

Sean A. Irvine, Table of n, a(n) for n = 2..108

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

Array[PrimeOmega[Subfactorial[#]] &, 40, 2]

lista(nmax) = {my(s = 0); for(n = 2, nmax, s = n * s + (-1)^n; print1(bigomega(s), ", "));}

a(n) = A001222(A000166(n)).

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

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

A378162 Number k such that !k = A000166(k) is squarefree.

Original entry on oeis.org

0, 2, 3, 6, 8, 11, 14, 15, 18, 20, 24, 27, 30, 32, 35, 36, 39, 42, 44, 47, 48, 54, 59, 60, 62, 63, 66, 68, 71, 72, 74, 75, 80, 83, 84, 86, 87, 90, 92, 95, 96, 98, 102, 104, 107, 108, 110, 114, 116

Offset: 1

Amiram Eldar, Nov 18 2024

0 and numbers k such that A378160(k) = A378161(k).
If k is a term, then k-1 is squarefree (since (k-1) | A000166(k)).
a(34) >= 83.

Cf. A000166, A005117, A378160, A378161.

Select[Range[0, 40], SquareFreeQ[Subfactorial[#]] &]

lista(kmax) = {my(s = 0); print1(0, ", "); for(k = 2, kmax, s = k * s + (-1)^k; if(issquarefree(s), print1(k, ", ")));}

a(34)-a(49) from Jinyuan Wang, Nov 25 2024

cp's OEIS Frontend

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

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula

Extensions