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A344622
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a(n) = n*(n+1)/2 - sigma(n) + d(n).
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0
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1, 2, 4, 6, 11, 13, 22, 25, 35, 41, 56, 56, 79, 85, 100, 110, 137, 138, 172, 174, 203, 221, 254, 248, 297, 313, 342, 356, 407, 401, 466, 471, 517, 545, 586, 584, 667, 685, 728, 738, 821, 815, 904, 912, 963, 1013, 1082, 1062, 1171, 1188, 1258, 1286, 1379, 1373, 1472, 1484
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OFFSET
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1,2
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COMMENTS
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For 1 <= k <= n, add 1 if k|n, otherwise add k. For example, a(12) = 1 + 1 + 1 + 1 + 5 + 1 + 7 + 8 + 9 + 10 + 11 + 1 = 56.
If p is prime, a(p) = p*(p+1)/2 - sigma(p) + d(p) = p*(p+1)/2 - (p+1) + 2 = 1 + p*(p-1)/2.
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LINKS
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FORMULA
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a(n) = Sum_{k=1..n} k^(ceiling(n/k)-floor(n/k)).
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EXAMPLE
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a(10) = 10*(10+1)/2 - sigma(10) + d(10) = 55 - 18 + 4 = 41.
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MATHEMATICA
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Table[n (n + 1)/2 - DivisorSigma[1, n] + DivisorSigma[0, n], {n, 80}]
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PROG
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(PARI) a(n) = n*(n+1)/2 - sigma(n) + numdiv(n); \\ Michel Marcus, May 25 2021
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CROSSREFS
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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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