A361662 - OEIS

%I #15 Jul 15 2023 14:55:37

%S 1,4,6,8,24,48,96,12,216,24,60,48,30,96,210,32,288,216,72,24,216,60,

%T 240,48,210,36,6480,96,15552,4320,7560,64,120,288,2520,216,5040,72,

%U 960,768,2520,216,576,60,83160,240,7680,48,18480,13860,7776,144,1152,6480

%N Least number k >= 1 such that A074206(k) is divisible by n.

%C a(n) exists for all n. (This is problem 5 of the first round of the British Mathematical Olympiad 2022/2023.)

%C All terms are in A025487.

%H Pontus von Brömssen, <a href="/A361662/b361662.txt">Table of n, a(n) for n = 1..10000</a>

%H British Mathematical Olympiad, <a href="https://bmos.ukmt.org.uk/home/bmo1-2023.pdf">Round 1</a>, Problem 5, 2022/2023.

%H <a href="/index/O#Olympiads">Index to sequences related to Olympiads</a>.

%F a(n) = A025487(A361663(n)).

%o (PARI) f(n)={if(!n, 0, my(sig=factor(n)[, 2], m=vecsum(sig)); sum(k=0, m, prod(i=1, #sig, binomial(sig[i]+k-1, k-1))*sum(r=k, m, binomial(r, k)*(-1)^(r-k))))}; \\ A074206

%o a(n) = my(k=1); while (f(k) % n, k++); k; \\ _Michel Marcus_, Mar 23 2023

%Y Cf. A025487, A074206, A361663, A361664, A361666.

%K nonn

%O 1,2

%A _Pontus von Brömssen_, Mar 20 2023