cp's OEIS Frontend

A322445 Smallest positive integer m such that n divides A297707(m).

%I A322445 #13 Feb 16 2025 08:33:57
%S A322445 1,2,3,4,5,3,7,4,3,5,11,4,13,7,5,4,17,3,19,5,7,11,23,4,5,13,6,7,29,5,
%T A322445 31,4,11,17,7,5,37,19,13,5,41,7,43,11,5,23,47,4,7,5,17,13,53,6,11,7,
%U A322445 19,29,59,5,61,31,7,4,13
%N A322445 Smallest positive integer m such that n divides A297707(m).
%C A322445 If p is prime, a(p) = p.
%C A322445 The first three integers n for which a(n!) is not a prime number are: 1 (a(1!) = 1), 4 (a(4!) = 4), 10 (a(10!) = 8). Is there a larger n? If such a number n exists, it is greater than 2000.
%C A322445 The smallest integer n satisfying the equation a(n) = a(n+1) is 2400 (a(2400) = a(2401) = 7). Is there a larger n? If such a number n exists, it is greater than 3000.
%H A322445 J. Sondow and E. W. Weisstein, <a href="https://mathworld.wolfram.com/SmarandacheFunction.html">MathWorld: Smarandache Function</a>
%e A322445 a(12) = 4 because 12 is not divisible by A297707(1) = 1, A297707(2) = 2*1, A297707(3) = 3*2*1*3*1, and is divisible by A297707(4) = 4*3*2*1*4*2*4*1.
%t A322445 f[n_] := n^(n - 1) *  Product[k^DivisorSigma[0, n - k], {k, n - 1}]; a[n_] := Module[{k = 1}, While[! Divisible[f[k], n], k++]; k]; Array[a, 60] (* _Amiram Eldar_, Dec 08 2018 *)
%o A322445 (PARI) f(n) = (n^(n-1))*prod(k=1, n-1, k^numdiv(n-k)); \\ A297707
%o A322445 a(n) = {my(k=1); while (f(k) % n, k++); k;} \\ _Michel Marcus_, Dec 09 2018
%Y A322445 Cf. A002034, A007922, A063917.
%K A322445 nonn
%O A322445 1,2
%A A322445 _Lechoslaw Ratajczak_, Dec 08 2018