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A091369
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a(n) = Sum_{i=1..n} phi(i)*ceiling(n/i).
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3
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1, 3, 7, 12, 20, 27, 39, 50, 64, 77, 97, 112, 136, 155, 177, 200, 232, 255, 291, 318, 350, 381, 425, 456, 500, 537, 581, 620, 676, 713, 773, 820, 872, 921, 979, 1026, 1098, 1153, 1215, 1270, 1350, 1403, 1487, 1550, 1618, 1685, 1777, 1840, 1930, 1999, 2081, 2156
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internal format)
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OFFSET
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1,2
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LINKS
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FORMULA
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MAPLE
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MATHEMATICA
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PROG
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(PARI) a(n) = sum(k=1, n, eulerphi(k)*ceil(n/k)); \\ Michel Marcus, Apr 13 2017
(Python)
from functools import lru_cache
@lru_cache(maxsize=None)
if n == 0:
return 0
c, j = 0, 2
k1 = n//j
while k1 > 1:
j2 = n//k1 + 1
c += (j2-j)*(2*A091369(k1)-(k1*(k1-1)+1))
j, k1 = j2, n//j2
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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