A143112 - OEIS

%I #7 Sep 25 2018 08:07:36

%S 1,2,2,4,2,6,2,8,5,8,2,14,2,10,8,16,2,18,2,20,10,14,2,30,7,16,14,26,2,

%T 32,2,32,14,20,10,44,2,22,16,44,2,42,2,38,26,26,2,62,9,38,20,44,2,54,

%U 14,58,22,32,2,80,2,34,34,64,16,62,2,56,26,58,2,96,2,40,38,62,14,72,2,92

%N A051731 * A032742 = sum of largest proper divisors of the divisors of n.

%C Inverse Möbius transform of A032742. - _Antti Karttunen_, Sep 25 2018

%H Antti Karttunen, <a href="/A143112/b143112.txt">Table of n, a(n) for n = 1..65537</a>

%F A051731 * A032742, where A051731 = the inverse Mobius transform and A032742 = the largest proper divisors of n: (1, 1, 1, 3, 1, 3, 1, 4, 3, 5, 1, 6, 1, 7,...).

%F a(n) = Sum_{d|n} A032742(d). - _Antti Karttunen_, Sep 25 2018

%e a(12) = 14. The divisors of 12 are shown in row 12 of triangle A127093: (1, 2, 3, 4, 0, 6, 0, 0, 0, 0, 0, 12). The largest proper divisors of these terms are (1, 1, 1, 2, 0, 3, 0, 0, 0, 0, 0, 6), sum = 14. Or, we can take row of triangle A051731: (1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1) dot (1, 1, 1, 2, 1, 3, 1, 4, 3, 5, 1, 6) = (1 + 1 + 1 + 2 + 0 + 3 + 0 + 0 + 0 + 0 + 0 + 6) = 14, where A032742 = (1, 1, 1, 2, 1, 3, 1, 4, 3, 5,...).

%o (PARI)

%o A032742(n) = if(1==n,n,n/vecmin(factor(n)[,1]));

%o A143112(n) = sumdiv(n,d,A032742(d)); \\ _Antti Karttunen_, Sep 25 2018

%Y Cf. A051731, A127093, A032742, A300236, A305807, A305808.

%K nonn

%O 1,2

%A _Gary W. Adamson_ and _Mats Granvik_, Jul 25 2008

%E More terms from _R. J. Mathar_, Jan 19 2009