A367476 - OEIS

%I #17 Jun 23 2024 02:12:28

%S 0,2,3,2,5,5,7,2,3,7,1,5,3,9,8,2,7,5,9,7,10,3,3,5,5,5,3,9,9,10,1,2,4,

%T 9,12,5,7,11,6,7,1,12,3,3,8,5,7,5,7,7,10,5,3,5,6,9,12,11,9,10,1,3,10,

%U 2,8,6,7,9,6,14,1,5,3,9,8,11,8,8,9,7,3,3,3,12,12

%N Sum of the final digits of the distinct prime divisors of n.

%C Even if a prime divides n more than once, it is only counted once.

%C Inverse Möbius transform of (n mod 10) * c(n), where c(n) is the prime characteristic (A010051). - _Wesley Ivan Hurt_, Jun 23 2024

%F a(n) = Sum_{p|n, p prime} (p mod 10).

%F a(n) = Sum_{d|n} (d mod 10) * c(d), where c = A010051. - _Wesley Ivan Hurt_, Jun 23 2024

%e a(66) = 6; The distinct prime divisors of 66 are 2, 3, 11 and the sum of their final digits is 2 + 3 + 1 = 6.

%t a[n_]:=Total[Mod[Select[Divisors[n],PrimeQ],10]]; Array[a,85] (* _Stefano Spezia_, Nov 19 2023 *)

%o (Python)

%o from sympy import factorint

%o def a(n): return sum(p%10 for p in factorint(n))

%o print([a(n) for n in range(1, 86)]) # _Michael S. Branicky_, Nov 19 2023

%o (PARI) a(n) = my(f=factor(n)); sum(k=1, #f~, f[k,1] % 10); \\ _Michel Marcus_, Nov 21 2023

%Y Cf. A008472, A010051, A010879 (final digit of n), A367466.

%K nonn,base,easy

%O 1,2

%A _Wesley Ivan Hurt_, Nov 19 2023