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A276736 a(n) = numerator of Sum_{d|n} tau(d)/d. 3
1, 2, 5, 11, 7, 10, 9, 13, 2, 14, 13, 55, 15, 18, 7, 57, 19, 4, 21, 77, 15, 26, 25, 65, 38, 30, 58, 99, 31, 14, 33, 15, 65, 38, 9, 11, 39, 42, 25, 91, 43, 30, 45, 13, 14, 50, 49, 95, 66, 76, 95, 165, 55, 116, 91, 117, 35, 62, 61, 77, 63, 66, 18, 247, 21, 130 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Also numerators of (Sum_{d|n} sigma(d)) / n.
LINKS
FORMULA
For all n we have: n = (Sum_{d|n} sigma(d)) / (Sum_{d|n} tau(d)/d) = (Sum_{d|n} d*tau(n/d)) / (Sum_{d|n} tau(d)/d) = A007429(n) * A276737(n) / a(n).
EXAMPLE
For n=6; {d_6} = {1, 2, 3, 6}; {tau(d)_6} = {1, 2, 2, 4}; Sum_{d|6} tau(d)/d = 1/1 + 2/2 + 2/3 + 4/6 = 20/6 = 10/3; a(6) = 10.
For n=6; {d_6} = {1, 2, 3, 6}; {sigma(d)_6} = {1, 3, 4, 12}; (Sum_{d|6} sigma(d))/6 = (1+3+4+12)/6 = 10/3; a(6) = 10.
MATHEMATICA
Table[Numerator@ Total[DivisorSigma[0, #]/#] &@ Divisors@ n, {n, 66}] (* Michael De Vlieger, Sep 16 2016 *)
PROG
(Magma) [Numerator(&+[NumberOfDivisors(d)/d: d in Divisors(n)]): n in [1..100]]
(PARI) a(n) = numerator(sumdiv(n, d, numdiv(d)/d)); \\ Michel Marcus, Sep 16 2016
CROSSREFS
Cf. A000005, A007429, A276737 (denominators).
Sequence in context: A127011 A170868 A357588 * A069162 A300677 A079008
KEYWORD
nonn,frac
AUTHOR
Jaroslav Krizek, Sep 16 2016
STATUS
approved

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Last modified March 2 17:21 EST 2024. Contains 370497 sequences. (Running on oeis4.)