A233284 -id:A233284 - cp's OEIS frontend

A055874 a(n) = largest m such that 1, 2, ..., m divide n.

1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 4, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 4, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 4, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 4, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 4, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 4, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 4, 1, 2, 1, 2

Offset: 1

Leroy Quet, Jul 16 2000

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.
A235921 gives such n where a(n^2) (= A235918(n)) differs from A071222(n-1) (= A053669(n)-1). (End)
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

			a(12) = 4 because 1, 2, 3, 4 divide 12, but 5 does not.

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.

One less than A007978.

Cf. also A053669, A055881, A055926, A017593, A064859, A181062, A126800, A232098, A232099, A233284, A235918, A235921.

a055874 n = length $ takeWhile ((== 0) . (mod n)) [1..]
-- Reinhard Zumkeller, Feb 21 2012, Dec 09 2010

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

a[n_] := Module[{m = 1}, While[Divisible[n, m++]]; m - 2]; Array[a, 100] (* Jean-François Alcover, Mar 07 2016 *)

a(n) = my(m = 1); while ((n % m) == 0, m++); m - 1; \\ Michel Marcus, Jan 17 2014

from itertools import count
def A055874(n):
    for m in count(1):
        if n % m:
            return m-1 # Chai Wah Wu, Jan 02 2022

(define (A055874 n) (let loop ((m 1)) (if (not (zero? (modulo n m))) (- m 1) (loop (+ 1 m))))) ;; Antti Karttunen, Nov 18 2013

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

A233285 a(n) = largest m such that m! divides n-th Fibonacci number; a(n) = A055881(A000045(n)).

Original entry on oeis.org

1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 4, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 4, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 4, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 4, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 6, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 4, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 4, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 4, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 4, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 7

Offset: 1

Antti Karttunen, Dec 06 2013

nonn

The lengths of palindromic prefixes begin as:
1, 2, 5, 8, 11, 23, 35, 47, 59, 119, 239, 359, 479, 959, 1439, 1919, ...
+1 results: 2, 3, 6, 9, 12, 24, 36, 48, 60, 120, 240, 360, 480, 960, 1440, 1920, ...

Antti Karttunen, Table of n, a(n) for n = 1..12600

Differs from A233284 for the first time at n=120, where a(120)=7, while A233284(120)=12.

Cf. A055881, A000045, A001175-A001177, A233283, A233281.

A233283 Record values in partial LCM-products (A233287) of Fibonacci entry points (A001177).

Original entry on oeis.org

1, 3, 12, 60, 120, 840, 2520, 12600, 239400, 2633400, 5266800, 15800400, 458211600, 7789597200, 288215096400, 3746796253200, 26227573772400, 131137868862000, 1049102950896000, 24129367870608000, 1906220061778032000, 78155022532899312000, 6955797005428038768000

Offset: 1

Antti Karttunen, Dec 13 2013

nonn

Conjecture: sequence gives the positions of records in A233284.

a(n+1)/a(n) = 3,4,5,2,7,3,5,19,11,2,3,29,17,37,13,7,5,8,23,79... - Ralf Stephan, Dec 17 2013

Antti Karttunen, Table of n, a(n) for n = 1..101

Cf. A233282, A233284, A233285, A233287.

(define (A233283 n) (A233287 (A233282 n)))

a(n) = A233287(A233282(n)).

A233287 a(n) = lcm_{i=1..n} A001177(i); partial LCM-products of Fibonacci entry points.

Original entry on oeis.org

1, 3, 12, 12, 60, 60, 120, 120, 120, 120, 120, 120, 840, 840, 840, 840, 2520, 2520, 2520, 2520, 2520, 2520, 2520, 2520, 12600, 12600, 12600, 12600, 12600, 12600, 12600, 12600, 12600, 12600, 12600, 12600, 239400, 239400, 239400, 239400, 239400, 239400, 2633400

Offset: 1

Antti Karttunen, Dec 13 2013

nonn

From n=3 onward it seems that lcm_{i=1..n} A001175(i) = 2*a(n).

Antti Karttunen, Table of n, a(n) for n = 1..1024
Index entries for sequences related to lcm's

Records occur at A233282. Cf. also A233283, A233284, A233285, A001175..A001177, A035105.

a(1)=1, and for n > 1, a(n) = lcm(A001177(n), a(n-1)).

a(n) = lcm_{i=1..n} A001177(i). [the least common multiple of all terms from A001177(1) to A001177(n)]

cp's OEIS Frontend

A055874 a(n) = largest m such that 1, 2, ..., m divide n.

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A233285 a(n) = largest m such that m! divides n-th Fibonacci number; a(n) = A055881(A000045(n)).

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A233283 Record values in partial LCM-products (A233287) of Fibonacci entry points (A001177).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Scheme

Formula

A233287 a(n) = lcm_{i=1..n} A001177(i); partial LCM-products of Fibonacci entry points.

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Author

Keywords

Comments

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Formula