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 A229829 Numbers coprime to 15. 11
 1, 2, 4, 7, 8, 11, 13, 14, 16, 17, 19, 22, 23, 26, 28, 29, 31, 32, 34, 37, 38, 41, 43, 44, 46, 47, 49, 52, 53, 56, 58, 59, 61, 62, 64, 67, 68, 71, 73, 74, 76, 77, 79, 82, 83, 86, 88, 89, 91, 92, 94, 97, 98, 101, 103, 104, 106, 107, 109, 112, 113, 116, 118, 119 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A001651 INTERSECT A047201. a(n) - 15*floor((n-1)/8) - 2*((n-1) mod 8) has period 8, repeating [1,0,0,1,0,1,1,0]. Numbers whose odd part is 7-rough: products of terms of A007775 and powers of 2 (terms of A000079). - Peter Munn, Aug 04 2020 The asymptotic density of this sequence is 8/15. - Amiram Eldar, Oct 18 2020 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). FORMULA a(n+8) = a(n) + 15. a(n) = 15*floor((n-1)/8) +2*f(n) +floor(2*phi*(f(n+1)+2)) -2*floor(phi*(f(n+1)+2)), where f(n) = (n-1) mod 8 and phi=(1+sqrt(5))/2. a(n) = 15*floor((n-1)/8) +2*f(n) +floor((2*f(n)+5)/5) -floor((f(n)+2)/3), where f(n) = (n-1) mod 8. From Bruno Berselli, Oct 01 2013: (Start) G.f.: x*(1 +x +2*x^2 +3*x^3 +x^4 +3*x^5 +2*x^6 +x^7 +x^8) / ((1-x)^2*(1+x)*(1+x^2)*(1+x^4)). - a(n) = a(n-1) +a(n-8) -a(n-9) for n>9. (End) Sum_{n>=1} (-1)^(n+1)/a(n) = 2*sqrt(7 + sqrt(5) - sqrt(6*(5 + sqrt(5))))*Pi/15. - Amiram Eldar, Dec 13 2021 MAPLE for n from 1 to 500 do if n mod 3<>0 and n mod 5<>0 then print(n) fi od MATHEMATICA Select[Range[120], GCD[#, 15] == 1 &] (* or *) t = 70; CoefficientList[Series[(1 + x + 2 x^2 + 3 x^3 + x^4 + 3 x^5 + 2 x^6 + x^7 + x^8)/((1 - x)^2 (1 + x) (1 + x^2) (1 + x^4)) , {x, 0, t}], x] (* Bruno Berselli, Oct 01 2013 *) Select[Range[120], CoprimeQ[#, 15]&] (* Harvey P. Dale, Oct 31 2013 *) PROG (Magma) [n: n in [1..120] | IsOne(GCD(n, 15))]; // Bruno Berselli, Oct 01 2013 (Sage) [i for i in range(120) if gcd(i, 15) == 1] # Bruno Berselli, Oct 01 2013 CROSSREFS Lists of numbers coprime to other semiprimes: A007310 (6), A045572 (10), A162699 (14), A160545 (21), A235933 (35). Cf. A008676, A078588, A113763, A160542, A160543, A160544. Subsequence of: A001651, A047201. Subsequences: A000079, A007775. Sequence in context: A323108 A187418 A161989 * A000069 A344602 A333975 Adjacent sequences: A229826 A229827 A229828 * A229830 A229831 A229832 KEYWORD nonn,easy AUTHOR Gary Detlefs, Oct 01 2013 STATUS approved

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Last modified September 16 19:55 EDT 2024. Contains 375977 sequences. (Running on oeis4.)