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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A306467 Let S(n)_k be the smallest positive integer t that t!k is a multiple of n (t!k is k-tuple factorial of t); then a(n) is the smallest k for which S(n)_k = n. 0
 1, 1, 1, 1, 1, 2, 1, 3, 2, 2, 1, 3, 1, 2, 3, 5, 1, 4, 1, 5, 3, 2, 1, 9, 4, 2, 7, 7, 1, 6, 1, 9, 3, 2, 5, 13, 1, 2, 3, 15, 1, 6, 1, 11, 10, 2, 1, 15, 6, 8, 3, 13, 1, 14, 5, 21, 3, 2, 1, 15, 1, 2, 14, 17, 5, 6, 1, 17, 3, 10, 1, 35, 1, 2, 12, 19, 7, 6, 1, 25 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS If p is prime, a(p) = 1. Conjecture: consecutive primes p satisfying the equation a(p+1) = 2 are consecutive elements of A005383 (primes p such that (p+1)/2 are also primes, for p > 3). The conjecture was checked for all primes < 10^4. Conjecture: consecutive primes p satisfying the equations a(p+1) = 2 and a(p+2) = 3 are consecutive elements of A036570 (primes p such that (p+1)/2 and (p+2)/3 are also primes). The conjecture was checked for all primes < 10^4. The first six solutions of the equation a(n) = a(n+1) are 1, 2, 3, 4, 9, 27. Is there a larger n? If such a number n exists, it is larger than 4000. LINKS Table of n, a(n) for n=1..80. J. Sondow and E. W. Weisstein, MathWorld: Smarandache Function EXAMPLE a(8) = 3 because: - for k = 1 is: 1!1, 2!1, 3!1 are not multiples of 8 and 4!1 is a multiple of 8, then (t = 4 = S(8)_1) <> (n = 8); - for k = 2 is: 1!2, 2!2, 3!2 are not multiples of 8 and 4!2 is a multiple of 8, then (t = 4 = S(8)_2) <> (n = 8); - for k = 3 is: 1!3, 2!3, 3!3, 4!3, 5!3, 6!3, 7!3 are not multiples of 8 and 8!3 is a multiple of 8, then (t = 8 = S(8)_3) = (n = 8), hence a(8) = k = 3. CROSSREFS Cf. A002034, A005383, A007922, A036570, A063917. Sequence in context: A109082 A324923 A126303 * A157810 A072339 A342507 Adjacent sequences: A306464 A306465 A306466 * A306468 A306469 A306470 KEYWORD nonn AUTHOR Lechoslaw Ratajczak, Feb 17 2019 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 April 20 10:23 EDT 2024. Contains 371818 sequences. (Running on oeis4.)