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A265392
a(n) = denominator of Sum_{d|n} 1 / tau(d).
7
1, 2, 2, 6, 2, 4, 2, 12, 6, 4, 2, 4, 2, 4, 4, 60, 2, 4, 2, 4, 4, 4, 2, 8, 6, 4, 12, 4, 2, 8, 2, 20, 4, 4, 4, 36, 2, 4, 4, 8, 2, 8, 2, 4, 4, 4, 2, 40, 6, 4, 4, 4, 2, 8, 4, 8, 4, 4, 2, 8, 2, 4, 4, 140, 4, 8, 2, 4, 4, 8, 2, 72, 2, 4, 4, 4, 4, 8, 2, 40, 60, 4, 2
OFFSET
1,2
COMMENTS
a(n) = denominator of Sum_{d|n} 1 / A000005(d).
LINKS
FORMULA
a(n) = A265391(n) / [Sum_{d|n} 1 / tau(d)] = A265391(n) * A253139(n) / A265390(n).
a(1) = 1; a(p) = 2 for p = prime; a(n) = n for numbers 1, 2, 36, 72, ...
EXAMPLE
For n = 6; divisors d of 6: {1, 2, 3, 6}; tau(d): {1, 2, 2, 4}; Sum_{d|6} 1 / tau(d) = 1/1 + 1/2 + 1/2 + 1/4 = 9 / 4; a(n) = 4 (denominator).
MATHEMATICA
Table[Denominator[Sum[1/DivisorSigma[0, d], {d, Divisors@ n}]], {n, 83}] (* Michael De Vlieger, Dec 09 2015 *)
PROG
(Magma) [Denominator(&+[1/NumberOfDivisors(d): d in Divisors(n)]): n in [1..1000]]
(PARI) a(n) = denominator(sumdiv(n, d, 1/numdiv(d))); \\ Michel Marcus, Dec 09 2015
CROSSREFS
Sequence in context: A349330 A367203 A068976 * A253139 A318519 A349356
KEYWORD
nonn,frac
AUTHOR
Jaroslav Krizek, Dec 08 2015
STATUS
approved