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A143615 Triangle A054521 * A000005 as a vector.

%I A143615 #17 Oct 02 2024 04:17:56
%S A143615 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 A143615 54,29,101,15,111,39,64,41,84,26,140,47,78,40,158,24,168,51,75,61,186,
%U A143615 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 A143615 Triangle A054521 * A000005 as a vector.
%F A143615 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 A143615 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 A143615 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 A143615 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 A143615 := proc(n)
%p A143615     local a,m;
%p A143615     a := 0 ;
%p A143615     for m from 1 to n do
%p A143615         if gcd(m,n) = 1 then
%p A143615         a := a+numtheory[tau](m) ;
%p A143615         end if;
%p A143615     end do:
%p A143615     a ;
%p A143615 end proc: # _R. J. Mathar_, Aug 08 2012
%Y A143615 Cf. A054521, A000005, A143614.
%K A143615 nonn
%O A143615 1,3
%A A143615 _Gary W. Adamson_, Aug 27 2008
%E A143615 More terms from _Naohiro Nomoto_, Aug 05 2012