OFFSET
1,2
COMMENTS
From Antti Karttunen, Nov 20 2013 & Jan 26 2014: (Start)
Differs from A232098 for the first time at n=840, where a(840)=8, while A232098(840)=7. A232099 gives all the differing positions. See also the comments at A055926 and A232099.
The positions where a(n) is an odd prime is given by A017593 up to A017593(34)=414 (so far all 3's), after which comes the first 7 at a(420). (A017593 gives the positions of 3's.)
(Continued on Jan 26 2014):
Only terms of A181062 occur as values.
a(n) is the largest m such that A003418(m) divides n. - David W. Wilson, Nov 20 2014
a(n) is the largest number of consecutive integers dividing n. - David W. Wilson, Nov 20 2014
A051451 gives indices where record values occur. - Gionata Neri, Oct 17 2015
Yuri Matiyasevich calls this the maximum inheritable divisor of n. - N. J. A. Sloane, Dec 14 2023
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..10080
Bakir Farhi, On the average asymptotic behavior of a certain type of sequences of integers, Integers, Vol. 9 (2009), pp. 555-567.
FORMULA
a(n) = A007978(n) - 1. - Antti Karttunen, Jan 26 2014
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = A064859 (Farhi, 2009). - Amiram Eldar, Jul 25 2022
EXAMPLE
a(12) = 4 because 1, 2, 3, 4 divide 12, but 5 does not.
MAPLE
N:= 1000: # to get a(1) to a(N)
A:= Vector(N, 1);
for m from 2 do
Lm:= ilcm($1..m);
if Lm > N then break fi;
if Lm mod (m+1) = 0 then next fi;
for k from 1 to floor(N/Lm) do
A[k*Lm]:=m
od
od:
convert(A, list); # Robert Israel, Nov 28 2014
MATHEMATICA
a[n_] := Module[{m = 1}, While[Divisible[n, m++]]; m - 2]; Array[a, 100] (* Jean-François Alcover, Mar 07 2016 *)
PROG
(Haskell)
a055874 n = length $ takeWhile ((== 0) . (mod n)) [1..]
-- Reinhard Zumkeller, Feb 21 2012, Dec 09 2010
(Scheme)
(define (A055874 n) (let loop ((m 1)) (if (not (zero? (modulo n m))) (- m 1) (loop (+ 1 m))))) ;; Antti Karttunen, Nov 18 2013
(PARI) a(n) = my(m = 1); while ((n % m) == 0, m++); m - 1; \\ Michel Marcus, Jan 17 2014
(Python)
from itertools import count
def A055874(n):
for m in count(1):
if n % m:
return m-1 # Chai Wah Wu, Jan 02 2022
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Leroy Quet, Jul 16 2000
STATUS
approved