%I #18 Jun 21 2024 17:48:08

%S 1,3,4,3,6,12,8,3,4,8,2,12,4,14,14,3,8,12,10,8,12,6,4,12,6,12,4,14,10,

%T 22,2,3,8,14,18,12,8,20,16,8,2,26,4,6,14,12,8,12,8,8,12,12,4,12,12,14,

%U 20,20,10,22,2,6,12,3,14,24,8,14,16,24,2,12,4,14,14,20

%N Sum of the final digits of the squarefree divisors of n.

%C Inverse Möbius transform of mu(n)^2 * (n mod 10). - _Wesley Ivan Hurt_, Jun 21 2024

%H Robert Israel, <a href="/A367503/b367503.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = Sum_{d|n} mu(d)^2 * (d mod 10).

%e a(10) = 8. The squarefree divisors of 10 are 1, 2, 5, 10 and the sum of their final digits is 1 + 2 + 5 + 0 = 8.

%p f:= proc(n) local t; add(t mod 10, t = map(convert,combinat:-powerset(numtheory:-factorset(n)),`*`)) end proc:

%p map(f, [$1..100]); # _Robert Israel_, Nov 21 2023

%t Table[DivisorSum[n, MoebiusMu[#]^2*Mod[#, 10] &], {n, 100}]

%o (PARI) a(n) = sumdiv(n, d, if (issquarefree(d), d%10)); \\ _Michel Marcus_, Nov 21 2023

%Y Cf. A005117 (squarefree numbers), A010879 (final digit of n), A367466 (sum of the final digits of the divisors of n), A371925 (numbers that occur in this sequence).

%K nonn,easy,base

%O 1,2

%A _Wesley Ivan Hurt_, Nov 20 2023