|
| |
|
|
A007978
|
|
Least non-divisor of n.
|
|
32
|
|
|
|
2, 3, 2, 3, 2, 4, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 4, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 4, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 4, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 4, 2, 3, 2, 3, 2, 7, 2, 3, 2, 3, 2, 4, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 4, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 4, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
Least k >= 2 such that sigma(n) divides sigma(n*k), where sigma is A000203. - Benoit Cloitre, Dec 01 2002
Contains all and only the prime powers p^k, k > 0. The first occurrence of p^k is at A003418(p^k-1); so new records occur at indices in A051451. - Franklin T. Adams-Watters, Jun 13 2011
|
|
|
LINKS
|
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
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) = A053669(n) + A061853(n) = A055874(n) + 1. - Henry Bottomley, May 10 2001
G.f.: sum(k >= 2, -k*(x^A003418(k) - x^A003418(k-1))/((x^A003418(k) - 1)*(x^A003418(k-1) - 1))). - Robert Israel, Sep 02 2014
From Alonso del Arte, Sep 23 2017: (Start)
a(n) < n for all n > 2.
a(2n + 1) = 2, a(2n) >= 3.
a(2^k) = 3 for k > 0.
a(n!) = prime(pi(n) + 1) for n >= 0, except for a(3!) = 4. (End)
Asymptotic mean: lim_{n->oo} Sum_{k=1..n} a(k) = 1 + A064859 (Farhi, 2009). - Amiram Eldar, Jun 29 2021
|
|
|
MAPLE
|
a:= proc(n) local k;
for k from 2 while n mod k = 0 do od:
k
end proc:
seq(a(n), n=1..100); # Robert Israel, Sep 02 2014
|
|
|
MATHEMATICA
|
Table[k := 1; While[Mod[n, k] == 0, k++]; k, {n, 2000}] (* Clark Kimberling, Jun 16 2012 *)
Join[{2, 3}, Table[Complement[Range[n], Divisors[n]][[1]], {n, 3, 100}]] (* Alonso del Arte, Sep 23 2017 *)
|
|
|
PROG
|
(Haskell)
import Data.List ((\\))
a007978 = head . ([1..] \\) . a027750_row
-- Reinhard Zumkeller, May 10 2014
(PARI) a(n) = {my(k=2); while(!(n % k), k++); k; } \\ Michel Marcus, Sep 25 2017
|
|
|
CROSSREFS
|
Cf. A003418, A051451, A055874, A053669, A061853, A027750, A064859.
Cf. also A266620 (least non-divisor of n!).
Sequence in context: A228829 A341982 A337686 * A245575 A333600 A339625
Adjacent sequences: A007975 A007976 A007977 * A007979 A007980 A007981
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
Jeffrey Shallit
|
|
|
STATUS
|
approved
|
| |
|
|
