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A083345 Numerator of r(n) = Sum(e/p: n=Product(p^e)). 6
0, 1, 1, 1, 1, 5, 1, 3, 2, 7, 1, 4, 1, 9, 8, 2, 1, 7, 1, 6, 10, 13, 1, 11, 2, 15, 1, 8, 1, 31, 1, 5, 14, 19, 12, 5, 1, 21, 16, 17, 1, 41, 1, 12, 13, 25, 1, 7, 2, 9, 20, 14, 1, 3, 16, 23, 22, 31, 1, 23, 1, 33, 17, 3, 18, 61, 1, 18, 26, 59, 1, 13, 1, 39, 11, 20, 18, 71, 1, 11, 4, 43, 1, 31, 22 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

The fraction a(n)/A083346(n) is totally additive with a(p) = 1/p. - Franklin T. Adams-Watters, May 17 2006

Least common multiple of n and its arithmetic derivative, divided by n, i.e. a(n) = lcm(n,n')/n = A086130(n)/A000027(n). - Giorgio Balzarotti, Apr 14 2011

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

EXAMPLE

n=12 = 2*2*3 = 2^2 * 3^1 --> r(12) = 2/2 + 1/3 = (6+2)/6, therefore a(12)=4, A083346(12)=3;

n=18 = 2*3*3 = 2^1 * 3^2 --> r(18) = 1/2 + 2/3 = (3+4)/6, therefore a(18)=7, A083346(18)=6.

MAPLE

with(numtheory): P:=proc(n) local a, k; a:=ifactors(n)[2];

numer(add(a[k][2]/a[k][1], k=1..nops(a))); end: seq(P(i), i=1..85); # Paolo P. Lava, Oct 17 2018

MATHEMATICA

Array[Numerator@ Total[FactorInteger[#] /. {p_, e_} /; e > 0 :> e/p] - Boole[# == 1] &, 85] (* Michael De Vlieger, Feb 25 2018 *)

PROG

(PARI) A083345(n) = { my(f=factor(n)); numerator(vecsum(vector(#f~, i, f[i, 2]/f[i, 1]))); }; \\ Antti Karttunen, Feb 25 2018

CROSSREFS

Cf. A083346 (denominator), A072873, A083347, A083348.

Sequence in context: A215010 A136744 A068237 * A087262 A082343 A166125

Adjacent sequences:  A083342 A083343 A083344 * A083346 A083347 A083348

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Apr 25 2003

STATUS

approved

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Last modified October 16 06:21 EDT 2019. Contains 328048 sequences. (Running on oeis4.)