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A372792
Number of divisors of 12n; a(n) = tau(12*n) = A000005(12*n).
11
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
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.
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}]
PROG
(PARI) A372792(n) = numdiv(12*n); \\ Antti Karttunen, Jul 19 2024
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, May 13 2024
STATUS
approved