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A291186 a(n) = numerator of (pod(n) / tau(n)). 4
1, 1, 3, 8, 5, 9, 7, 16, 9, 25, 11, 288, 13, 49, 225, 1024, 17, 972, 19, 4000, 441, 121, 23, 41472, 125, 169, 729, 10976, 29, 101250, 31, 16384, 1089, 289, 1225, 1119744, 37, 361, 1521, 320000, 41, 388962, 43, 42592, 30375, 529, 47, 127401984, 343, 62500, 2601 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
pod(n) = the product of the divisors of n (A007955), tau(n) = the number of the divisors of n (A000005).
LINKS
FORMULA
a(n) = numerator of (A007955(n) / A000005(n)).
EXAMPLE
For n = 4; pod(4) / tau(4) = 8 / 3; a(n) = 8.
MAPLE
f:= proc(n) local D; D:= numtheory:-divisors(n); numer(convert(D, `*`)/nops(D)) end proc:
map(f, [$1..100]); # Robert Israel, Sep 14 2017
MATHEMATICA
Table[Numerator[Apply[Times, Divisors@ n]/DivisorSigma[0, n]], {n, 51}] (* Michael De Vlieger, Sep 05 2017 *)
PROG
(Magma) [Numerator(&*[d: d in Divisors(n)] / #[d: d in Divisors(n)]): n in [1..1000]]
(PARI) a(n) = my(d=divisors(n)); numerator(prod(k=1, #d, d[k])/#d); \\ Michel Marcus, Sep 05 2017
CROSSREFS
Cf. A137927 (denominator).
Sequence in context: A342934 A256616 A323707 * A347942 A058055 A229598
KEYWORD
nonn,frac
AUTHOR
Jaroslav Krizek, Sep 05 2017
STATUS
approved

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Last modified February 21 14:42 EST 2024. Contains 370236 sequences. (Running on oeis4.)