A143615 - OEIS

%I #17 Oct 02 2024 04:17:56

%S 1,1,3,3,8,3,14,7,14,8,27,7,35,12,20,18,50,11,58,16,35,24,74,15,68,29,

%T 54,29,101,15,111,39,64,41,84,26,140,47,78,40,158,24,168,51,75,61,186,

%U 34,170,49,111,66,217,39,160,65,131,80,247,32,261,84,122,92,197,45,292,92,162,60,312,55,326,104,135,106,263,55,356,85,206

%N Triangle A054521 * A000005 as a vector.

%F Triangle A054521 * A000005 as a vector; where 1's indicate the relative primes of n by rows and A000005 = d(n): (1, 2, 2, 3, 2, 4, 2, 4, 3,...)

%F a(n) = Sum_{ m=1..n and gcd(n,m)=1 } tau(m), where tau(m)=A000005(m). A211932(n)+a(n) = A006218(n). - _Naohiro Nomoto_, Aug 05 2012

%e a(8) = 7 since the relative primes of 8 are (1, 3, 5, 7). a(8) = d(1) + d(3) + d(5) + d(7) = 1 + 2 + 2 + 2. Or, a(8) = 7 = (1, 0, 1, 0, 1, 0, 1, 0) dot (1, 2, 2, 3, 2, 4, 2, 4), where (1, 0, 1, 0, 1, 0, 1, 0) = row 8 of triangle A054521 and d(n) = (1, 2, 2, 3, 2, 4, 2, 4, 3, 4, 2,...).

%e a(7) = 14 = (1, 1, 1, 1, 1, 1, 0) dot (1, 2, 2, 3, 2, 4, 2) = (d(1) + d(2) + d(3) + d(4) + d(5) + d(6)).

%p A143615 := proc(n)

%p     local a,m;

%p     a := 0 ;

%p     for m from 1 to n do

%p         if gcd(m,n) = 1 then

%p         a := a+numtheory[tau](m) ;

%p         end if;

%p     end do:

%p     a ;

%p end proc: # _R. J. Mathar_, Aug 08 2012

%Y Cf. A054521, A000005, A143614.

%K nonn

%O 1,3

%A _Gary W. Adamson_, Aug 27 2008

%E More terms from _Naohiro Nomoto_, Aug 05 2012