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A160353 Numbers of the form p*q*r, where p < q < r are odd primes such that r = +/-1 (mod p*q). 4

%I #12 Aug 04 2023 23:16:31

%S 435,465,861,885,903,915,1335,1743,2211,2235,2265,2485,2667,2685,2715,

%T 3081,3165,3507,3585,3615,4035,4065,4323,4431,4865,4965,5151,5253,

%U 5271,5385,5835,5995,6123,6153,6285,6315,6441,6501,6567,6735,7077,7185,7385

%N Numbers of the form p*q*r, where p < q < r are odd primes such that r = +/-1 (mod p*q).

%C Kaplan (2007) has shown that this is a subsequence of A117223 (and thus of A160350; see there for the reference), i.e., the cyclotomic polynomial phi(n) has coefficients in {0,1,-1} for indices n listed here.

%C This is a subsequence of A160352 which drops the requirement that p > 2.

%C See A160350 for further details and references.

%H Robin Visser, <a href="/A160353/b160353.txt">Table of n, a(n) for n = 1..10000</a>

%e a(1) = 435 = 3*5*29 is the smallest product of odd primes p < q < r such that r is congruent to +/- 1 modulo the product of the smaller factors, p*q.

%o (PARI) forstep( pqr=1,9999,2, my(f=factor(pqr)); #f~==3 & vecmax(f[,2])==1 & abs((f[3,1]+1)%(f[1,1]*f[2,1])-1)==1 & print1(pqr","))

%K nonn

%O 1,1

%A _M. F. Hasler_, May 11 2009

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Last modified April 20 03:03 EDT 2024. Contains 371798 sequences. (Running on oeis4.)