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A028235 If n = Product (p_j^k_j), a(n) = numerator of Sum 1/p_j (the denominator of this sum is A007947). 4
0, 1, 1, 1, 1, 5, 1, 1, 1, 7, 1, 5, 1, 9, 8, 1, 1, 5, 1, 7, 10, 13, 1, 5, 1, 15, 1, 9, 1, 31, 1, 1, 14, 19, 12, 5, 1, 21, 16, 7, 1, 41, 1, 13, 8, 25, 1, 5, 1, 7, 20, 15, 1, 5, 16, 9, 22, 31, 1, 31, 1, 33, 10, 1, 18, 61, 1, 19, 26, 59, 1, 5, 1, 39, 8, 21, 18, 71, 1, 7, 1, 43, 1, 41, 22, 45, 32 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

For n=1, the empty sum = 0 = 0/1 = a(1)/A007947(1), thus a(1) should be 0. - Antti Karttunen, Mar 04 2018

LINKS

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

FORMULA

Fraction is additive with a(p^e) = 1/p.

MAPLE

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

numer(add(1/a[k][1], k=1..nops(a))); end: seq(P(i), i=1..87); # Paolo P. Lava, Oct 17 2018

MATHEMATICA

a[1] = 0; a[n_] := 1/FactorInteger[n][[All, 1]] // Total // Numerator;

Array[a, 100] (* Jean-Fran├žois Alcover, May 08 2019 *)

PROG

(PARI) A028235(n) = numerator(vecsum(apply(p->(1/p), factor(n)[, 1]))); \\ Antti Karttunen, Mar 04 2018

CROSSREFS

Cf. A007947.

Sequence in context: A284254 A309206 A250097 * A028236 A066504 A292771

Adjacent sequences:  A028232 A028233 A028234 * A028236 A028237 A028238

KEYWORD

nonn,frac,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Erich Friedman.

Term a(1) changed to 0 by Antti Karttunen, Mar 04 2018

STATUS

approved

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Last modified April 9 20:46 EDT 2020. Contains 333363 sequences. (Running on oeis4.)