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

1,2

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.

Formula

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

Prog

(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

Crossrefs

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

Sequence in context: A074125 A063719 A272862 * A106366 A019160 A126233

Adjacent sequences: A361659 A361660 A361661 * A361663 A361664 A361665

Keyword

nonn

Author

Pontus von Brömssen, Mar 20 2023

Status

approved