A187336 -id:A187336 - cp's OEIS frontend

0, 0, 4, 7, 12, 14, 18, 21, 28, 28, 32, 35, 40, 42, 46, 49, 56, 56, 60, 63, 68, 70, 74, 77, 84, 84, 88, 91, 96, 98, 102, 105, 112, 112, 116, 119, 124, 126, 130, 133, 140, 140, 144, 147, 152, 154, 158, 161, 168, 168

Offset: 0

Gary Detlefs, Jun 30 2014

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).
Listed sequences of this form are:
G(n,2) ... A004526;
G(3,n) ... A130481;
G(n,4) ... A187326;
G(n,5) ... A187333;
G(n,6) ... A187336;
G(n,7) ... A187337;
G(n,k*n)/k = n*(n-1)/2  = G(n,n+k)-G(n,k).
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.

Cf. A109004.

[&+[Floor(k*n/8): k in [1..7]]: n in [0..50]]; // Bruno Berselli, Jul 01 2014

G:=(n,m)-> sum(floor(k*n/m), k=1..m-1): seq(G(n,8), n = 0..60);

Table[Sum[Floor[k n/8], {k, 1, 7}], {n, 0, 50}] (* Bruno Berselli, Jul 01 2014 *)

[sum(floor(k*n/8) for k in (1..7)) for n in (0..50)] # Bruno Berselli, Jul 01 2014

a(n) = sum( floor(k*n/8), k=1..7 ).
a(n) = ( gcd(n,8) - (n+8) + n*8 )/2.
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]

Some terms corrected by Bruno Berselli, Jul 01 2014

cp's OEIS Frontend

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

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