A073855 -id:A073855 - cp's OEIS frontend

A036430 Number of iterations needed to reach 1 under the map n -> Omega(n).

0, 1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 3, 1, 2, 1, 2, 2, 2, 1, 3, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 3, 1, 2, 2, 3, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 3, 2, 3, 2, 2, 1, 3, 1, 2, 2, 3, 2, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 1, 2, 3, 2, 1, 3, 2, 2, 2, 3, 1, 3, 2, 2, 2, 2, 2, 3, 1, 2, 2, 3, 1, 2, 1, 3, 2

Offset: 1

Dann Toliver

			16 -> 4 -> 2 -> 1 and thus a(16) = 3.

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A029908, A073855.

a(n)=my(s);while(n>1,n=bigomega(n);s++);s \\ Charles R Greathouse IV, Apr 25 2012

a(n) = a(bigomega(n)) + 1 for n > 1. - Vladeta Jovovic, Jul 10 2004

a(n) = O(log* n). - Charles R Greathouse IV, Apr 25 2012

Corrected and extended by Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 21 2003

Formula corrected by Charles R Greathouse IV, Apr 25 2012

A287841 Number of iterations of number of distinct prime factors (A001221) needed to reach 1 starting at n (n is counted).

Original entry on oeis.org

1, 2, 2, 2, 2, 3, 2, 2, 2, 3, 2, 3, 2, 3, 3, 2, 2, 3, 2, 3, 3, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 2, 3, 3, 3, 3, 2, 3, 3, 3, 2, 3, 2, 3, 3, 3, 2, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 3, 2, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 3, 2, 3, 2, 3, 3, 3, 3, 3, 2, 3, 2, 3, 2, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 2, 3, 2, 3, 3

Offset: 1

Ilya Gutkovskiy, Jun 01 2017

nonn

			If n = 6 the trajectory is {6, 2, 1}. Its length is 3, thus a(6) = 3.

Antti Karttunen, Table of n, a(n) for n = 1..16384
Eric Weisstein's World of Mathematics, Distinct Prime Factors
Index entries for sequences computed from exponents in factorization of n

Cf. A001221, A036430, A036459, A049108, A073855, A115658 (first occurrence), A246655 (positions of 2).

f[n_] := Length[NestWhileList[ PrimeNu, n, # != 1 &]]; Array[f, 105]
a[1] = 1; a[n_] := a[n] = a[PrimeNu[n]] + 1; Table[a[n], {n, 105}]

A287841(n) = if(1==n,n,1+A287841(omega(n))); \\ Antti Karttunen, Nov 23 2017

from sympy import primefactors
def a(n): return 1 if n==1 else a(len(primefactors(n))) + 1 # Indranil Ghosh, Jun 03 2017

a(n) = a(omega(n)) + 1 for n > 1, where omega() is the number of distinct prime factors.

cp's OEIS Frontend

A036430 Number of iterations needed to reach 1 under the map n -> Omega(n).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

PARI

Formula

Extensions