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A161203
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n-th square plus n-th squarefree number.
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2
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2, 6, 12, 21, 31, 43, 59, 75, 94, 114, 136, 161, 188, 217, 247, 279, 315, 353, 391, 431, 474, 518, 564, 613, 663, 715, 770, 826, 884, 946, 1008, 1075, 1142, 1211, 1282, 1354, 1428, 1505, 1583
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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LINKS
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FORMULA
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EXAMPLE
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a(1) = 1^2 + 1.
a(2) = 2^2 + 2.
a(3) = 3^2 + 3.
a(4) = 4^2 + 5.
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MATHEMATICA
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Module[{nn=40, sqs, sfree}, sqs=Range[nn]^2; sfree=Take[Select[Range[3nn], SquareFreeQ], nn]; Total/@Thread[{sqs, sfree}]] (* Harvey P. Dale, May 06 2012 *)
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PROG
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(Python)
from math import isqrt
from sympy import mobius
def f(x): return n+x-sum(mobius(k)*(x//k**2) for k in range(1, isqrt(x)+1))
m, k = n, f(n)
while m != k:
m, k = k, f(k)
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CROSSREFS
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KEYWORD
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nonn,easy,changed
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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