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A345093
a(n) = Sum_{d^2|n} n^abs(mu(n-d)).
0
1, 2, 3, 8, 1, 6, 7, 16, 10, 1, 11, 24, 1, 14, 15, 33, 1, 36, 1, 21, 1, 22, 23, 48, 2, 1, 28, 29, 1, 30, 31, 65, 1, 34, 35, 144, 1, 38, 39, 80, 1, 42, 43, 88, 46, 1, 47, 97, 50, 2, 1, 53, 1, 108, 1, 57, 1, 58, 59, 120, 1, 62, 64, 67, 1, 66, 67, 136, 1, 70, 71, 288, 1, 74, 150
OFFSET
1,2
FORMULA
If p is prime, a(p) = Sum_{d^2|p} p^abs(mu(p-d)) = p^abs(mu(p-1)).
EXAMPLE
a(8) = Sum_{d^2|8} 8^abs(mu(8-d)) = 8^abs(mu(7)) + 8^abs(mu(6)) = 8^1 + 8^1 = 16.
MATHEMATICA
Table[Sum[n^(MoebiusMu[n - k]^2) (1 - Ceiling[n/k^2] + Floor[n/k^2]), {k, n}], {n, 100}]
PROG
(PARI) a(n) = if (n==1, 1, sumdiv(n, d, if (issquare(d), n^abs(moebius(n-sqrtint(d)))))); \\ Michel Marcus, Jun 08 2021
CROSSREFS
Cf. A008683 (mu).
Sequence in context: A202688 A021046 A138180 * A079585 A354854 A354861
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jun 07 2021
STATUS
approved