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A352482 Denominator of (n-d)/n*d where d = A000005(n) is the number of divisors of n. 3
1, 1, 6, 12, 10, 12, 14, 8, 9, 20, 22, 12, 26, 28, 60, 80, 34, 9, 38, 60, 84, 44, 46, 12, 75, 52, 108, 84, 58, 120, 62, 96, 132, 68, 140, 12, 74, 76, 156, 10, 82, 168, 86, 132, 90, 92, 94, 240, 147, 75, 204, 156, 106, 216, 220, 28, 228, 116, 118, 15, 122, 124, 126, 448, 260, 264, 134 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
The terms are of course the denominators of the fraction "in smallest terms", otherwise said: a(n) = n*d/gcd(n*d, n - d), which is unambiguous also for n = 1 and n = 2 where n - d = 0.
LINKS
M. F. Hasler, Table of n, a(n) for n = 1..10000 (terms a(3..10^4) from Michel Marcus), Apr 17 2022
EXAMPLE
The number n = 1 has d = 1 divisors, so (n-d)/(n*d) = 0/1 has denominator a(1) = 1.
The number n = 2 has d = 2 divisors, so (n-d)/(n*d) = 0/4 = 0/1 has denominator a(2) = 1 when written in smallest terms.
The number n = 3 has d = 2 divisors, so (n-d)/(n*d) = 1/6 has denominator a(3) = 6.
The number n = 4 has d = 3 divisors, so (n-d)/(n*d) = 1/12 has denominator a(4) = 12.
The number n = 6 has d = 4 divisors, so (n-d)/(n*d) = 2/24 = 1/12 has denominator a(6) = 12.
MATHEMATICA
a[n_] := Numerator[n*(d = DivisorSigma[0, n])/(n - d)]; Array[a, 100, 3] (* Amiram Eldar, Mar 18 2022 *)
PROG
(PARI) A352482(n, d=numdiv(n))=denominator((n-d)/(n*d))
CROSSREFS
Cf. A000005, A049820, A146566, A352483 (numerator).
Sequence in context: A242549 A315777 A279606 * A164378 A124349 A360719
KEYWORD
nonn,frac
AUTHOR
Michel Marcus, Mar 18 2022
EXTENSIONS
Edited and extended to offset 1 by M. F. Hasler, Apr 17 2022
STATUS
approved

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Last modified February 25 05:01 EST 2024. Contains 370310 sequences. (Running on oeis4.)