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A337328
Number of pairs of squarefree divisors of n, (d1,d2), such that d1 <= d2.
0
1, 3, 3, 3, 3, 10, 3, 3, 3, 10, 3, 10, 3, 10, 10, 3, 3, 10, 3, 10, 10, 10, 3, 10, 3, 10, 3, 10, 3, 36, 3, 3, 10, 10, 10, 10, 3, 10, 10, 10, 3, 36, 3, 10, 10, 10, 3, 10, 3, 10, 10, 10, 3, 10, 10, 10, 10, 10, 3, 36, 3, 10, 10, 3, 10, 36, 3, 10, 10, 36, 3, 10, 3, 10, 10, 10, 10, 36
OFFSET
1,2
FORMULA
a(n) = Sum_{d1|n, d2|n, d1 and d2 squarefree, d1 <= d2} 1.
EXAMPLE
a(28) = 10; The divisors of 28 are {1,2,4,7,14,28}. The pairs of squarefree divisors of 28, (d1,d2), such that d1 <= d2 are (1,1), (1,2), (1,7), (1,14), (2,2), (2,7), (2,14), (7,7), (7,14) and (14,14). So a(28) = 10.
a(29) = 3; The divisors of 29 are {1,29}. The pairs of squarefree divisors of 29, (d1,d2), such that d1 <= d2 are (1,1), (1,29) and (29,29). So a(29) = 3.
a(30) = 36; The divisors of 30 are {1,2,3,5,6,10,15,30}. The 36 pairs of squarefree divisors of 30, (d1,d2) such that d1 <= d2 are (1,1), (1,2), (1,3), (1,5), (1,6), (1,10), (1,15), (1,30), (2,2), (2,3), (2,5), (2,6), (2,10), (2,15), (2,30), (3,3), (3,5), (3,6), (3,10), (3,15), (3,30), (5,5), (5,6), (5,10), (5,15), (5,30), (6,6), (6,10), (6,15), (6,30), (10,10), (10,15), (10,30), (15,15), (15,30), (30,30). So a(30) = 36.
a(31) = 3; The divisors of 31 are {1,31}. The pairs of squarefree divisors of 31 are (1,1), (1,31) and (31,31). So a(31) = 3.
MATHEMATICA
Table[Sum[Sum[MoebiusMu[i]^2 MoebiusMu[k]^2*(1 - Ceiling[n/k] + Floor[n/k]) (1 - Ceiling[n/i] + Floor[n/i]), {i, k}], {k, n}], {n, 100}]
CROSSREFS
Sequence in context: A111575 A161836 A087576 * A201700 A087575 A001270
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Aug 23 2020
STATUS
approved