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A345743
a(n) = Sum_{k=1..n} n^abs(mu(k)).
1
1, 4, 9, 13, 21, 31, 43, 50, 57, 73, 91, 100, 121, 144, 169, 181, 209, 222, 253, 267, 301, 337, 375, 392, 409, 451, 469, 487, 533, 581, 631, 652, 705, 760, 817, 841, 901, 963, 1027, 1054, 1121, 1190, 1261, 1291, 1321, 1396, 1473, 1505, 1537, 1569, 1651, 1684, 1769, 1803
OFFSET
1,2
COMMENTS
For all k <= n, add n if k is squarefree, otherwise add 1. For n = 12, the 8 squarefree numbers less than or equal to 12 are 1, 2, 3, 5, 6, 7, 10, and 11. This means that 4 are not squarefree, which gives a(12) = 12*8 + 4 = 100.
MATHEMATICA
Table[Sum[n^Abs[MoebiusMu[k]], {k, n}], {n, 80}]
PROG
(PARI) a(n) = sum(k=1, n, if (issquarefree(k), n, 1)); \\ Michel Marcus, Jun 26 2021
CROSSREFS
Cf. A008683 (mu), A345745.
Sequence in context: A312985 A312986 A240692 * A022130 A042125 A041905
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jun 25 2021
STATUS
approved