A008367 Composite but smallest prime factor >= 17.

289, 323, 361, 391, 437, 493, 527, 529, 551, 589, 629, 667, 697, 703, 713, 731, 779, 799, 817, 841, 851, 893, 899, 901, 943, 961, 989, 1003, 1007, 1037, 1073, 1081, 1121, 1139, 1147, 1159, 1189, 1207, 1219, 1241, 1247, 1271, 1273, 1333, 1343, 1349, 1357, 1363, 1369, 1387, 1403, 1411, 1457

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Composite numbers k such that k^720 mod 30030 = 1. - Gary Detlefs, May 02 2012

The asymptotic density of this sequence is 192/1001. - Amiram Eldar, Mar 22 2021

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A002808 and A008366.

Cf. A038511, A084969, A084970.

Cf. A287391.

Programs

GAP

Filtered([17..1500],n->PowerMod(n,720,30030)=1 and not IsPrime(n)); # Muniru A Asiru, Nov 24 2018

Maple

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

Mathematica

Select[ Range[ 1500 ], (GCD[ #1, 30030 ]==1&&!PrimeQ[ #1 ])& ]
Select[Range[2000], ! PrimeQ[#] && FactorInteger[#][[1, 1]] >= 17 &] (* T. D. Noe, Mar 16 2013 *)

PARI

is(n)={gcd(n,30030)==1 && !ispseudoprime(n)} \\ M. F. Hasler, Oct 04 2018

Formula

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