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A318876
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Sum of divisors d of n for which 2*phi(d) > d.
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4
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1, 1, 4, 1, 6, 4, 8, 1, 13, 6, 12, 4, 14, 8, 24, 1, 18, 13, 20, 6, 32, 12, 24, 4, 31, 14, 40, 8, 30, 24, 32, 1, 48, 18, 48, 13, 38, 20, 56, 6, 42, 32, 44, 12, 78, 24, 48, 4, 57, 31, 72, 14, 54, 40, 72, 8, 80, 30, 60, 24, 62, 32, 104, 1, 84, 48, 68, 18, 96, 48, 72, 13, 74, 38, 124, 20, 96, 56, 80, 6, 121, 42, 84, 32, 108, 44, 120, 12, 90, 78, 112, 24, 128, 48, 120, 4, 98, 57, 156, 31, 102, 72, 104, 14, 87
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OFFSET
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1,3
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COMMENTS
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Not multiplicative as a(3) = 4, a(5) = 6 and a(7) = 8, but a(105) = 87, not a(3)*a(5)*a(7) = 4*6*8 = 192 = A000593(105).
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LINKS
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FORMULA
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a(n) = Sum_{d|n} [2*phi(d) > d]*d, where [ ] are the Iverson brackets.
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EXAMPLE
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n = 105 has divisors [1, 3, 5, 7, 15, 21, 35, 105]. When A083254 is applied to them, all others except the last one result a positive number, thus a(105) = 1+3+5+7+15+21+35 = 87.
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PROG
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(PARI) A318876(n) = sumdiv(n, d, ((2*eulerphi(d))>d)*d);
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CROSSREFS
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Differs from A000593 for the first time at n=105, where a(105) = 87, while A000593(105) = 192.
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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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