OFFSET
1,3
COMMENTS
It is easy to show that n divides psi(n) for all n.
For k >= 2, n^k divides psi(n^(k+1)) if and only if n is not of the form 2*(p_1)^(e_1)*(p_2)^(e_2)*...*(p_m)^(e_m), where p_i are distinct odd primes not congruent to 1 modulo 2^k.
It seems that every positive integer occurs in this sequence. The first occurrence of each k is given by A341860.
LINKS
Jianing Song, Table of n, a(n) for n = 1..10000
FORMULA
For odd n > 1, a(2n) = a(n)/2.
EXAMPLE
psi(220^2) = psi(2^4 * 5^2 * 11^2) = lcm(psi(2^4), psi(5^2), psi(11^2)) = lcm(4, 20, 110) = 220, so a(220) = psi(220^2)/220 = 220/220 = 1.
MATHEMATICA
Array[CarmichaelLambda[#^2]/# &, 100] (* Paolo Xausa, Mar 11 2024 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Jianing Song, Feb 21 2021
STATUS
approved