A367466 -id:A367466 - cp's OEIS frontend

A367503 Sum of the final digits of the squarefree divisors of n.

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

Offset: 1

Wesley Ivan Hurt, Nov 20 2023

Inverse Möbius transform of mu(n)^2 * (n mod 10). - Wesley Ivan Hurt, Jun 21 2024

			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.

Robert Israel, Table of n, a(n) for n = 1..10000

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).

f:= proc(n) local t;  add(t mod 10, t = map(convert,combinat:-powerset(numtheory:-factorset(n)),`*`)) end proc:
map(f, [$1..100]); # Robert Israel, Nov 21 2023

Table[DivisorSum[n, MoebiusMu[#]^2*Mod[#, 10] &], {n, 100}]
Table[Total[Mod[Select[Divisors[n],SquareFreeQ],10]],{n,100}] (* Harvey P. Dale, Jun 06 2025 *)

a(n) = sumdiv(n, d, if (issquarefree(d), d%10)); \\ Michel Marcus, Nov 21 2023

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

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

Original entry on oeis.org

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

Wesley Ivan Hurt, Nov 19 2023

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

			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.

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

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

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

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

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

cp's OEIS Frontend

A367503 Sum of the final digits of the squarefree divisors of n.

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