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A084969 Numbers whose smallest prime factor is 11.

%I A084969 #60 Dec 08 2020 03:49:35
%S A084969 11,121,143,187,209,253,319,341,407,451,473,517,583,649,671,737,781,
%T A084969 803,869,913,979,1067,1111,1133,1177,1199,1243,1331,1397,1441,1507,
%U A084969 1529,1573,1639,1661,1727,1793,1837,1859,1903,1969,1991,2057,2101,2123,2167,2189,2299,2321
%N A084969 Numbers whose smallest prime factor is 11.
%C A084969 Fifth row of A083140.
%C A084969 Integers k such that gcd(11*k, 210) = 1.
%H A084969 Amiram Eldar, <a href="/A084969/b084969.txt">Table of n, a(n) for n = 1..10000</a>
%H A084969 <a href="/index/Rec#order_49">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1).
%F A084969 G.f.: 11*x*(x^48 +10*x^47 +2*x^46 +4*x^45 +2*x^44 +4*x^43 +6*x^42 +2*x^41 +6*x^40 +4*x^39 +2*x^38 +4*x^37 +6*x^36 +6*x^35 +2*x^34 +6*x^33 +4*x^32 +2*x^31 +6*x^30 +4*x^29 +6*x^28 +8*x^27 +4*x^26 +2*x^25 +4*x^24 +2*x^23 +4*x^22 +8*x^21 +6*x^20 +4*x^19 +6*x^18 +2*x^17 +4*x^16 +6*x^15 +2*x^14 +6*x^13 +6*x^12 +4*x^11 +2*x^10 +4*x^9 +6*x^8 +2*x^7 +6*x^6 +4*x^5 +2*x^4 +4*x^3 +2*x^2 +10*x +1) / (x^49 -x^48 -x +1). - _Colin Barker_, Feb 22 2013
%F A084969 a(n) = a(n-48) + 2310 = a(n-1) + a(n-48) - a(n-49). - _Charles R Greathouse IV_, Nov 19 2014
%F A084969 Lim_{n->infinity} a(n)/n = A038111(5)/A038110(5) = 385/8 = 48.125. - _Vladimir Shevelev_, Jan 20 2015
%F A084969 a(n) = 11*A008364(n).
%e A084969 a(2) = 11*11, a(3) = 11*13.
%t A084969 11Select[ Range[210], GCD[ #, 2*3*5*7] == 1 & ]
%t A084969 Select[11*Range[0,200],GCD[#,210]==1&] (* _Harvey P. Dale_, Dec 23 2013 *)
%o A084969 (PARI) is(n)=gcd(n,2310)==11 \\ _Charles R Greathouse IV_, Nov 19 2014
%Y A084969 Cf. A084967 (5), A084968 (7), A084970 (13), A332799 (17), A332798 (19), A332797 (23), A008364 (11-rough numbers).
%Y A084969 Cf. A008364, A038110, A038111, A083140.
%K A084969 nonn,easy
%O A084969 1,1
%A A084969 _Robert G. Wilson v_, Jun 15 2003
%E A084969 a(47)-a(49) from _Georg Fischer_, Nov 07 2019
%E A084969 New name from _Frank Ellermann_, Feb 25 2020