A367503 - OEIS

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

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OFFSET

1,2

COMMENTS

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

LINKS

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

FORMULA

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

EXAMPLE

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.

MAPLE

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

MATHEMATICA

Table[DivisorSum[n, MoebiusMu[#]^2*Mod[#, 10] &], {n, 100}]

PROG

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

CROSSREFS

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).

Sequence in context: A218789 A324335 A238162 * A048250 A323363 A073181

Adjacent sequences: A367500 A367501 A367502 * A367504 A367505 A367506

KEYWORD

nonn,easy,base

AUTHOR

Wesley Ivan Hurt, Nov 20 2023

STATUS

approved