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A008367 Composite but smallest prime factor >= 17. 3

%I

%S 289,323,361,391,437,493,527,529,551,589,629,667,697,703,713,731,779,

%T 799,817,841,851,893,899,901,943,961,989,1003,1007,1037,1073,1081,

%U 1121,1139,1147,1159,1189,1207,1219,1241,1247,1271,1273,1333,1343,1349,1357,1363,1369,1387,1403,1411,1457

%N Composite but smallest prime factor >= 17.

%C Composite numbers k such that k^720 mod 30030 = 1. - _Gary Detlefs_, May 02 2012

%C The asymptotic density of this sequence is 192/1001. - _Amiram Eldar_, Mar 22 2021

%H T. D. Noe, <a href="/A008367/b008367.txt">Table of n, a(n) for n = 1..10000</a>

%F For 1 <= n < 107, a(n) = A287391(n+2); then a(107) = 2329, a(108) = 2363 are not in A287391, but again a(n) = A287391(n) for 108 < n < 120. - _M. F. Hasler_, Oct 04 2018

%p for i from 1 to 2000 do if gcd(i,30030) = 1 and not isprime(i) then print(i); fi; od;

%t Select[ Range[ 1500 ], (GCD[ #1, 30030 ]==1&&!PrimeQ[ #1 ])& ]

%t Select[Range[2000], ! PrimeQ[#] && FactorInteger[#][[1, 1]] >= 17 &] (* _T. D. Noe_, Mar 16 2013 *)

%o (PARI) is(n)={gcd(n,30030)==1 && !ispseudoprime(n)} \\ _M. F. Hasler_, Oct 04 2018

%o (GAP) Filtered([17..1500],n->PowerMod(n,720,30030)=1 and not IsPrime(n)); # _Muniru A Asiru_, Nov 24 2018

%Y Intersection of A002808 and A008366.

%Y Cf. A038511, A084969, A084970.

%Y Cf. A287391.

%K nonn

%O 1,1

%A _N. J. A. Sloane_.

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Last modified June 25 10:28 EDT 2021. Contains 345453 sequences. (Running on oeis4.)