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A278049
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a(n) = 3*(Sum_{k=1..n} phi(k)) - 1, where phi = A000010.
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1
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2, 5, 11, 17, 29, 35, 53, 65, 83, 95, 125, 137, 173, 191, 215, 239, 287, 305, 359, 383, 419, 449, 515, 539, 599, 635, 689, 725, 809, 833, 923, 971, 1031, 1079, 1151, 1187, 1295, 1349, 1421, 1469, 1589, 1625, 1751, 1811, 1883, 1949, 2087, 2135, 2261, 2321, 2417, 2489, 2645, 2699, 2819, 2891, 2999
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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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G.f.: (1/(1 - x)) * (-x + 3 * Sum_{k>=1} mu(k) * x^k / (1 - x^k)^2). - Ilya Gutkovskiy, Feb 14 2020
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MAPLE
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with(numtheory);
f:=n->3*add(phi(r), r=1..n)-1;
[seq(f(r), r=1..50)];
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MATHEMATICA
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PROG
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(Python)
from functools import lru_cache
@lru_cache(maxsize=None)
if n == 0:
return -1
c, j = 0, 2
k1 = n//j
while k1 > 1:
j2 = n//k1 + 1
j, k1 = j2, n//j2
return 3*(n*(n-1)-c+j)//2 - 1 # Chai Wah Wu, Mar 25 2021
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CROSSREFS
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Cf. m*(Sum_{k=1..n} phi(k)) - 1: A015614 (m=1), A018805 (m=2), this sequence (m=3).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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