A367476 Sum of the final digits of the distinct prime divisors of n.

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

Offset: 1

Author

Wesley Ivan Hurt, Nov 19 2023

Keywords

• nonn
• base
• easy

Comments

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

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

Examples

			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.
		

Crossrefs

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

Programs

Mathematica

a[n_]:=Total[Mod[Select[Divisors[n],PrimeQ],10]]; Array[a,85] (* Stefano Spezia, Nov 19 2023 *)

PARI

a(n) = my(f=factor(n)); sum(k=1, #f~, f[k,1] % 10); \\ Michel Marcus, Nov 21 2023

Python

from sympy import factorint
def a(n): return sum(p%10 for p in factorint(n))
print([a(n) for n in range(1, 86)]) # Michael S. Branicky, Nov 19 2023

Formula

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

a(n) = Sum_{d|n} (d mod 10) * c(d), where c = A010051. - Wesley Ivan Hurt, Jun 23 2024