A084968 Multiples of 7 coprime to 30.

7, 49, 77, 91, 119, 133, 161, 203, 217, 259, 287, 301, 329, 343, 371, 413, 427, 469, 497, 511, 539, 553, 581, 623, 637, 679, 707, 721, 749, 763, 791, 833, 847, 889, 917, 931, 959, 973, 1001, 1043, 1057, 1099, 1127, 1141, 1169, 1183, 1211, 1253, 1267, 1309

Offset: 1

Author

Robert G. Wilson v, Jun 15 2003

Keywords

• nonn
• easy

Comments

Numbers 7*k such that gcd(k,30) = 1.

Numbers congruent to 7, 49, 77, 91, 119, 133, 161, 203 modulo 210. - Jianing Song, Nov 18 2022

Examples

			77 is in the sequence because gcd(77, 30) = 1.
84 is not in the sequence because gcd(84, 3) = 6.
91 is in the sequence because gcd(91, 30) = 1.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,1,-1).

Crossrefs

Subsequence of A008589.

Fourth row of A083140.

Cf. A084967 (5), A084969 (11), A084970 (13), A332799 (17), A332798 (19), A332797 (23), A007775 (7-rough numbers).

Programs

Maple

q:= k-> igcd(k, 30)=1:
select(q, [7*i$i=1..300])[];  # Alois P. Heinz, Feb 25 2020

Mathematica

7Select[ Range[190], GCD[ #, 2*3*5] == 1 & ]

PARI

is(n)=gcd(210,n)==7 \\ Charles R Greathouse IV, Aug 05 2013

Formula

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

Lim_{n->oo} a(n)/n = A038111(4)/A038110(4) = 105/4. - Vladimir Shevelev, Jan 20 2015

a(n) = 7*A007775(n).

a(n+8) = a(n) + 210. - Jianing Song, Nov 18 2022

Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(23 + sqrt(5) - sqrt(6*(5 + sqrt(5))))*Pi/105. - Amiram Eldar, Jul 15 2023