A361662 Least number k >= 1 such that A074206(k) is divisible by n.

1, 4, 6, 8, 24, 48, 96, 12, 216, 24, 60, 48, 30, 96, 210, 32, 288, 216, 72, 24, 216, 60, 240, 48, 210, 36, 6480, 96, 15552, 4320, 7560, 64, 120, 288, 2520, 216, 5040, 72, 960, 768, 2520, 216, 576, 60, 83160, 240, 7680, 48, 18480, 13860, 7776, 144, 1152, 6480

Offset: 1

Author

Pontus von Brömssen, Mar 20 2023

Keywords

• nonn

Comments

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

All terms are in A025487.

Links

• Pontus von Brömssen, Table of n, a(n) for n = 1..10000
• British Mathematical Olympiad, Round 1, Problem 5, 2022/2023.
• Index to sequences related to Olympiads.

Crossrefs

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

Programs

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
a(n) = my(k=1); while (f(k) % n, k++); k; \\ Michel Marcus, Mar 23 2023

Formula

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