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A084968
Multiples of 7 coprime to 30.
17
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
1,1
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
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
EXAMPLE
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.
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 & ]
PROG
(PARI) is(n)=gcd(210, n)==7 \\ Charles R Greathouse IV, Aug 05 2013
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).
Sequence in context: A083930 A178367 A036132 * A161145 A343737 A344473
KEYWORD
nonn,easy
AUTHOR
Robert G. Wilson v, Jun 15 2003
STATUS
approved