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A244590 a(n) = sum( floor(k*n/8), k=1..7 ).

%I A244590 #23 Sep 08 2022 08:46:08
%S A244590 0,0,4,7,12,14,18,21,28,28,32,35,40,42,46,49,56,56,60,63,68,70,74,77,
%T A244590 84,84,88,91,96,98,102,105,112,112,116,119,124,126,130,133,140,140,
%U A244590 144,147,152,154,158,161,168,168
%N A244590 a(n) = sum( floor(k*n/8), k=1..7 ).
%C A244590 This sequence is G(n,8) where G(n,m) = sum(floor(k*n/m), k=1..m-1). This function is referenced in A109004 and is used in the following formula for gcd(n,m): gcd(n,m) = n+m-n*m+2*G(n,m).
%C A244590 Listed sequences of this form are:
%C A244590 G(n,2) ... A004526;
%C A244590 G(3,n) ... A130481;
%C A244590 G(n,4) ... A187326;
%C A244590 G(n,5) ... A187333;
%C A244590 G(n,6) ... A187336;
%C A244590 G(n,7) ... A187337;
%C A244590 G(n,k*n)/k = n*(n-1)/2  = G(n,n+k)-G(n,k).
%C A244590 It is of interest to note that this alternate form of gcd(n,m) will be undefined if m is a function having a zero in it. For example, gcd(n, n mod 4) would be undefined but gcd(n mod 4, n) would be defined.
%F A244590 a(n) = sum( floor(k*n/8), k=1..7 ).
%F A244590 a(n) = ( gcd(n,8) - (n+8) + n*8 )/2.
%F A244590 G.f.: x^2*(4 + 3*x + 5*x^2 + 2*x^3 + 4*x^4 + 3*x^5 + 7*x^6)/((1 + x)*(1 - x)^2*(1 + x^2)*(1 + x^4)). [_Bruno Berselli_, Jul 01 2014]
%p A244590 G:=(n,m)-> sum(floor(k*n/m), k=1..m-1): seq(G(n,8), n = 0..60);
%t A244590 Table[Sum[Floor[k n/8], {k, 1, 7}], {n, 0, 50}] (* _Bruno Berselli_, Jul 01 2014 *)
%o A244590 (Magma) [&+[Floor(k*n/8): k in [1..7]]: n in [0..50]]; // _Bruno Berselli_, Jul 01 2014
%o A244590 (Sage) [sum(floor(k*n/8) for k in (1..7)) for n in (0..50)] # _Bruno Berselli_, Jul 01 2014
%Y A244590 Cf. A109004.
%K A244590 nonn,easy
%O A244590 0,3
%A A244590 _Gary Detlefs_, Jun 30 2014
%E A244590 Some terms corrected by _Bruno Berselli_, Jul 01 2014