The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A007978 Least non-divisor of n. 33
 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 (Python) def a(n): k = 2 while not n%k: k += 1 return k print([a(n) for n in range(1, 101)]) # Michael S. Branicky, Jul 09 2022 (Python) def A007978(n): return next(filter(lambda d:n%d, range(2, n))) if n>2 else n+1 # Chai Wah Wu, Feb 22 2023 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 23 00:10 EDT 2023. Contains 365532 sequences. (Running on oeis4.)