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A372792
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a(n) = tau(12*n) = A000005(12*n).
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10
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6, 8, 9, 10, 12, 12, 12, 12, 12, 16, 12, 15, 12, 16, 18, 14, 12, 16, 12, 20, 18, 16, 12, 18, 18, 16, 15, 20, 12, 24, 12, 16, 18, 16, 24, 20, 12, 16, 18, 24, 12, 24, 12, 20, 24, 16, 12, 21, 18, 24, 18, 20, 12, 20, 24, 24, 18, 16, 12, 30, 12, 16, 24, 18, 24, 24
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OFFSET
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1,1
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COMMENTS
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In general, for m>=1, Sum_{j=1..n} tau(m*j) = A018804(m) * n * log(n) + O(n).
If p is prime, then Sum_{j=1..n} tau(p*j) ~ (2*p - 1) * n * (log(n) - 1 + 2*gamma)/p + n*log(p)/p, where gamma is the Euler-Mascheroni constant A001620.
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LINKS
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FORMULA
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Sum_{k=1..n} a(k) ~ (40*n*(log(n) + 2*gamma - 1) + n*(20*log(2) + 8*log(3))) / 12, where gamma is the Euler-Mascheroni constant A001620.
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MATHEMATICA
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Table[DivisorSigma[0, 12*n], {n, 1, 150}]
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CROSSREFS
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Cf. A000005, A099777, A372713, A372784, A372785, A372786, A372787, A372788, A372789, A372790, A372791.
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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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