This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A359070 #12 Feb 07 2023 15:16:41 %S A359070 3,4,15,12,39,54,79,86,144,318,1591,144,20131,2014,1764,1308,46656, %T A359070 1296 %N A359070 Smallest k > 1 such that k^n - 1 is the product of n distinct primes. %C A359070 a(19) > 60000 and a(20) = 3940. %C A359070 a(19) > 5 * 10^5; a(21) = 132023; a(22) = 229430; a(24) = 4842. - _Daniel Suteu_, Dec 16 2022 %C A359070 Because of the algebraic factorization of x^n-1 (via cyclotomic polynomials), there is good reason to expect (on average) that prime values of n will have larger solutions than other numbers. That is, those values of n with many factors already get a head start by having many algebraic factors. - _Sean A. Irvine_, Jan 06 2023 %F A359070 a(n) >= A219019(n). - _Daniel Suteu_, Dec 16 2022 %e A359070 a(3) = 15 since 15^3 - 1 = 3374 = 2*7*241 is the product of 3 distinct primes and 15 is the smallest number with this property. %o A359070 (PARI) isok(k, n) = my(f=factor(k^n - 1)); issquarefree(f) && (omega(f) == n); %o A359070 a(n) = my(k=2); while (!isok(k, n), k++); k; \\ _Michel Marcus_, Dec 15 2022 %Y A359070 Cf. A001597, A005117, A045542, A219019, A281940, A359069. %K A359070 nonn,hard,more %O A359070 1,1 %A A359070 _Kevin P. Thompson_, Dec 15 2022