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A372792 a(n) = tau(12*n) = A000005(12*n). 10
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
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.
LINKS
FORMULA
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.
MATHEMATICA
Table[DivisorSigma[0, 12*n], {n, 1, 150}]
CROSSREFS
Sequence in context: A138103 A043373 A054047 * A056653 A285847 A231879
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, May 13 2024
STATUS
approved

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Last modified June 27 20:20 EDT 2024. Contains 373753 sequences. (Running on oeis4.)