Search: id:A007775
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%I A007775
%S A007775 1,7,11,13,17,19,23,29,31,37,41,43,47,49,53,59,61,67,71,73,77,79,
%T A007775 83,89,91,97,101,103,107,109,113,119,121,127,131,133,137,139,143,149,151,
               157,
%U A007775 161,163,167,169,173,179,181,187,191,193,197,199,203,209
%N A007775 Not divisible by 2, 3 or 5.
%C A007775 Also numbers n such that the sum of the 4-th powers of the first n positive 
               integers is divisible by n, or A000538(n) = n*(n+1)(2*n+1)(3*n^2+3*n-1)/
               30 is divisible by n. - Alexander Adamchuk (alex(AT)kolmogorov.com), 
               Jan 04 2007
%C A007775 A141256(a(n)) = n+1. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Jun 17 2008
%C A007775 Also the 7-rough numbers: positive integers that have no prime factors 
               less than 7 [From Michael Porter (michael_b_porter(AT)yahoo.com), 
               Oct 09 2009]
%H A007775 N. J. A. Sloane, <a href="b007775.txt">Table of n, a(n) for n = 1..8000</
               a>
%H A007775 Theodore E. Hahn, <a href="http://www.ebookmall.com/ebooks/showdetl.cfm?&DID=8&Product_ID=29054">
               Title?</a>
%H A007775 Theodore E. Hahn, <a href="http://www.hahnalei.net/graylight/avta_and_chi_numbers.htm">
               Title?</a>
%H A007775 Theodore E. Hahn, <a href="http://www.hahnalei.net/graylight/code/math/
               avta/Sequences.html">Title?</a>
%H A007775 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               RoughNumber.html">Rough Number</a> From MathWorld--A Wolfram Web 
               Resource. [From Michael Porter (michael_b_porter(AT)yahoo.com), Oct 
               09 2009]
%H A007775 <a href="Sindx_Sk.html#smooth">Index entries for sequences related to 
               smooth numbers</a> [From Michael Porter (michael_b_porter(AT)yahoo.com), 
               Oct 09 2009]
%F A007775 a(n+8)=a(n)+30. a(n)=a(n-1)+a(n-8)-a(n-9). G.f.: x*(1+6*x+4*x^2+2*x^3+4*x^4+2*x^5+4*x^6+6*x^7+x^8)/
               ((1+x)*(x^2+1)*(x^4+1)*( x-1)^2). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Feb 27 2009]
%p A007775 for i from 1 to 500 do if gcd(i,30) = 1 then print(i); fi; od;
%t A007775 Select[ Range[ 300 ], GCD[ #1, 30 ]==1& ]
%o A007775 (PARI) isA007775(n) = gcd(n,30)==1 [From Michael Porter (michael_b_porter(AT)yahoo.com), 
               Oct 09 2009]
%Y A007775 Cf. A000538, A054403.
%Y A007775 Cf. A008364, A008365, A008366. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Feb 27 2009]
%Y A007775 For k-rough numbers with other values of k, see A000027 A005408 A007310 
               A007775 A008364 A008365 A008366 A166061 A166063 [From Michael Porter 
               (michael_b_porter(AT)yahoo.com), Oct 09 2009]
%Y A007775 Sequence in context: A128974 A005776 A161850 this_sequence A070884 A135777 
               A090459
%Y A007775 Adjacent sequences: A007772 A007773 A007774 this_sequence A007776 A007777 
               A007778
%K A007775 nonn,easy
%O A007775 1,2
%A A007775 N. J. A. Sloane (njas(AT)research.att.com).

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