cp's OEIS Frontend

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.

A129295 Numbers m such that m^3 - 1 has no divisors d with 1 < d < m - 1.

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%I A129295 #12 May 26 2019 19:14:15
%S A129295 3,4,6,8,12,14,20,24,38,54,62,80,90,110,138,150,164,168,192,194,272,
%T A129295 278,314,332,348,398,402,434,500,572,642,644,720,728,762,798,812,860,
%U A129295 864,878,920,992,1020,1022,1070,1092,1098,1118,1130,1182,1202,1230,1260,1308
%N A129295 Numbers m such that m^3 - 1 has no divisors d with 1 < d < m - 1.
%C A129295 Numbers m such that A129294(m) = #{1,m-1} = 2.
%C A129295 Essentially the same as A096175. Note that m^3 - 1 = (m - 1)*(m^2 + m + 1), so m - 1 must be prime. For m > 4, the smallest divisor > 1 of m^2 + m + 1 is no larger than sqrt(m^2 + m + 1) < m + 1 unless m^2 + m + 1 is also prime. Also note that gcd(m, m^2 + m 1 ) = gcd(m - 1, m^2 + m + 1) = 1, so m^2 + m + 1 must also be prime, making m^3 - 1 a semiprime. - _Jianing Song_, Aug 01 2018
%F A129295 a(n) = A096175(n-2) for n > 2. - _Jianing Song_, Aug 01 2018
%e A129295 {1,11,157,1727} is the set of divisors of 12^3 - 1, therefore 12 is a term, since A129294(12) = #{1,11} = 2.
%Y A129295 Cf. A096175, A129293, A129294.
%K A129295 nonn
%O A129295 1,1
%A A129295 _Reinhard Zumkeller_, Apr 09 2007