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A067435
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a(n) is the sum of all the remainders when n-th odd number is divided by odd numbers < 2n-1.
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5
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0, 0, 2, 3, 6, 9, 16, 13, 27, 31, 34, 43, 57, 56, 75, 80, 96, 99, 121, 122, 155, 164, 163, 184, 220, 218, 255, 252, 277, 304, 339, 328, 372, 389, 412, 433, 491, 478, 515, 536, 570, 609, 638, 647, 722, 713, 746, 767, 858, 842, 910, 939, 942, 993, 1060, 1057
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OFFSET
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1,3
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LINKS
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FORMULA
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EXAMPLE
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a(7) = 16 = 1 +3 +6 +4 +2 = 13 % 3 + 13 % 5 + 13 % 7 + 13 % 9 + 13 % 11.
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MAPLE
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L:= [seq(4*n-3 - numtheory:-sigma(2*n-1)-numtheory:-sigma((n-1)/2^padic:-ordp(n-1, 2)), n=1..100)]:
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PROG
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(Python)
from math import isqrt
def A327329(n): return -(s:=isqrt(n))**2*(s+1)+sum((q:=n//k)*((k<<1)+q+1) for k in range(1, s+1))
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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Corrected and extended by several contributors.
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STATUS
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approved
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