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A367476
Sum of the final digits of the distinct prime divisors of n.
0
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
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
KEYWORD
nonn,base,easy
AUTHOR
Wesley Ivan Hurt, Nov 19 2023
STATUS
approved