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A055874
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a(n) = largest m such that 1, 2, ..., m divide n.
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43
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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
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OFFSET
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1,2
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COMMENTS
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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 number of consecutive integers dividing n. - David W. Wilson, Nov 20 2014
Yuri Matiyasevich calls this the maximum inheritable divisor of n. - N. J. A. Sloane, Dec 14 2023
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LINKS
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FORMULA
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Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = A064859 (Farhi, 2009). - Amiram Eldar, Jul 25 2022
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EXAMPLE
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a(12) = 4 because 1, 2, 3, 4 divide 12, but 5 does not.
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MAPLE
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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:
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MATHEMATICA
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a[n_] := Module[{m = 1}, While[Divisible[n, m++]]; m - 2]; Array[a, 100] (* Jean-François Alcover, Mar 07 2016 *)
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PROG
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(Haskell)
a055874 n = length $ takeWhile ((== 0) . (mod n)) [1..]
(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
for m in count(1):
if n % m:
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CROSSREFS
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Cf. also A053669, A055881, A055926, A017593, A064859, A181062, A126800, A232098, A232099, A233284, A235918, A235921.
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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