

A352482


Denominator of (nd)/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
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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



EXAMPLE

The number n = 1 has d = 1 divisors, so (nd)/(n*d) = 0/1 has denominator a(1) = 1.
The number n = 2 has d = 2 divisors, so (nd)/(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 (nd)/(n*d) = 1/6 has denominator a(3) = 6.
The number n = 4 has d = 3 divisors, so (nd)/(n*d) = 1/12 has denominator a(4) = 12.
The number n = 6 has d = 4 divisors, so (nd)/(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((nd)/(n*d))


CROSSREFS



KEYWORD

nonn,frac


AUTHOR



EXTENSIONS

Edited and extended to offset 1 by M. F. Hasler, Apr 17 2022


STATUS

approved



