OFFSET
1,1
COMMENTS
(ii) Equals composite numbers with {18, 2*p (p prime), p^i (p primes, i >= 2} deleted.
The second conjecture asserts that this is equal to A265128 with {0, 1, 18} deleted.
I believe I have a proof of both conjectures, although I have not yet written out all the details.
Numbers k that are in A265128, but do not appear here are: 1, 18, 50, 54, 98, 162, 242, 250, 338, 486, 578, 686, ... probably given by {1} UNION A354929. Hence conjecture: the sequence consists of numbers that are neither a power of prime, or 2 * power of prime. - Antti Karttunen, Jun 14 2022
Is this the set of all k such that Phi_k(-1) = Phi_k(0) = Phi_k(1) where Phi_k denotes the k-th cyclotomic polynomial? - Jeppe Stig Nielsen, Jun 26 2023
LINKS
N. J. A. Sloane, Table of n, a(n) for n = 1..8020
PROG
(PARI)
A047994(n) = { my(f=factor(n)~); prod(i=1, #f, (f[1, i]^f[2, i])-1); };
isA346608(n) = !A354924(n); \\ Antti Karttunen, Jun 13 2022
(PARI) isA346608conjectured(n) = ((n>1) && !isprimepower(n) && ((n%2) || !isprimepower(n/2)));
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Aug 09 2021
STATUS
approved