%I #71 Jul 15 2023 05:51:48
%S 7,49,77,91,119,133,161,203,217,259,287,301,329,343,371,413,427,469,
%T 497,511,539,553,581,623,637,679,707,721,749,763,791,833,847,889,917,
%U 931,959,973,1001,1043,1057,1099,1127,1141,1169,1183,1211,1253,1267,1309
%N Multiples of 7 coprime to 30.
%C Numbers 7*k such that gcd(k,30) = 1.
%C Numbers congruent to 7, 49, 77, 91, 119, 133, 161, 203 modulo 210. - _Jianing Song_, Nov 18 2022
%H Amiram Eldar, <a href="/A084968/b084968.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,1,-1).
%F G.f.: 7*x*(x^8 + 6*x^7 + 4*x^6 + 2*x^5 + 4*x^4 + 2*x^3 + 4*x^2 + 6*x + 1) / ((x-1)^2*(x+1)*(x^2+1)*(x^4+1)). - _Colin Barker_, Feb 24 2013
%F Lim_{n->oo} a(n)/n = A038111(4)/A038110(4) = 105/4. - _Vladimir Shevelev_, Jan 20 2015
%F a(n) = 7*A007775(n).
%F a(n+8) = a(n) + 210. - _Jianing Song_, Nov 18 2022
%F Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(23 + sqrt(5) - sqrt(6*(5 + sqrt(5))))*Pi/105. - _Amiram Eldar_, Jul 15 2023
%e 77 is in the sequence because gcd(77, 30) = 1.
%e 84 is not in the sequence because gcd(84, 3) = 6.
%e 91 is in the sequence because gcd(91, 30) = 1.
%p q:= k-> igcd(k, 30)=1:
%p select(q, [7*i$i=1..300])[]; # _Alois P. Heinz_, Feb 25 2020
%t 7Select[ Range[190], GCD[ #, 2*3*5] == 1 & ]
%o (PARI) is(n)=gcd(210,n)==7 \\ _Charles R Greathouse IV_, Aug 05 2013
%Y Subsequence of A008589.
%Y Fourth row of A083140.
%Y Cf. A084967 (5), A084969 (11), A084970 (13), A332799 (17), A332798 (19), A332797 (23), A007775 (7-rough numbers).
%K nonn,easy
%O 1,1
%A _Robert G. Wilson v_, Jun 15 2003