cp's OEIS Frontend

A306657 Least primary Carmichael number (A324316) with n prime factors, or -1 if no such number exists.

%I A306657 #22 Apr 22 2024 08:12:18
%S A306657 1729,10606681,4872420815346001
%N A306657 Least primary Carmichael number (A324316) with n prime factors, or -1 if no such number exists.
%C A306657 Primary Carmichael numbers were introduced in Kellner and Sondow 2019. For this sequence, see Kellner 2019.
%C A306657 Conjecture: the sequence is infinite.
%C A306657 a(6) > 10^22, if it exists. - _Amiram Eldar_, Apr 22 2024
%H A306657 Bernd C. Kellner and Jonathan Sondow, <a href="https://doi.org/10.4169/amer.math.monthly.124.8.695">Power-Sum Denominators</a>, Amer. Math. Monthly, 124 (2017), 695-709; <a href="https://arxiv.org/abs/1705.03857">arXiv preprint</a>, arXiv:1705.03857 [math.NT], 2017.
%H A306657 Bernd C. Kellner and Jonathan Sondow, <a href="http://math.colgate.edu/~integers/v52/v52.pdf">On Carmichael and polygonal numbers, Bernoulli polynomials, and sums of base-p digits</a>, Integers 21 (2021), #A52, 21 pp.; <a href="https://arxiv.org/abs/1902.10672">arXiv preprint</a>, arXiv:1902.10672 [math.NT], 2019-2021.
%H A306657 Bernd C. Kellner, <a href="http://math.colgate.edu/~integers/w38/w38.pdf">On primary Carmichael numbers</a>, Integers 22 (2022), #A38, 39 pp.; <a href="https://arxiv.org/abs/1902.11283">arXiv preprint</a>, arXiv:1902.11283 [math.NT], 2019-2022.
%H A306657 <a href="/index/Ca#Carmichael">Index entries for sequences related to Carmichael numbers</a>.
%e A306657 1729 = 7 * 13 * 19,
%e A306657 10606681 = 31 * 43 * 73 * 109,
%e A306657 4872420815346001 = 211 * 239 * 379 * 10711 * 23801.
%Y A306657 Least Carmichael number with n prime factors is A006931.
%Y A306657 Cf. also A002997, A324316.
%K A306657 nonn,hard,more,bref
%O A306657 3,1
%A A306657 _Bernd C. Kellner_ and _Jonathan Sondow_, Mar 03 2019
%E A306657 Escape clause added by _Amiram Eldar_, Apr 22 2024