OFFSET
1,1
COMMENTS
Let a = p_1 * p_2 *...* p_k and b = q_1 * q_2 *...* q_k be two Charmichael numbers (A002997) with the same number of factors, where p_1 < p_2 <...< p_k and q_1 < q_2 <...< q_k are primes. We say that a and b are in the same family iff the vectors [p_1 - 1, ..., p_k - 1] and [q_1 - 1, ..., q_k - 1] are parallel. In other words, the ratios (p_1-1):(p_2-1):...:(p_k-1) and (q_1-1):(q_2-1):...:(q_k-1) are equal. Sequence gives Carmichael numbers that are NOT minimal in their family.
Not a subsequence of A328935 (for example 965507554621 is primitive but not minimal).
LINKS
EXAMPLE
294409 = 37*73*109 is a Carmichael number, belonging to family 36:72:108 = 1:2:3. However, 1729 = 7*13*19 is smaller Carmichael number, and the family 6:12:18 = 1:2:3 is the same. Therefore 294409 belongs to this sequence.
PROG
CROSSREFS
KEYWORD
nonn
AUTHOR
Jeppe Stig Nielsen, Apr 21 2021
STATUS
approved