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

1,2

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

Links

Table of n, a(n) for n=1..85.

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A035361 A137851 A369742 * A141346 A095402 A086294

Adjacent sequences: A367473 A367474 A367475 * A367477 A367478 A367479

Keyword

nonn,base,easy

Author

Wesley Ivan Hurt, Nov 19 2023

Status

approved