

A034460


a(n) = usigma(n)  n, where usigma(n) = sum of unitary divisors of n (A034448).


48



0, 1, 1, 1, 1, 6, 1, 1, 1, 8, 1, 8, 1, 10, 9, 1, 1, 12, 1, 10, 11, 14, 1, 12, 1, 16, 1, 12, 1, 42, 1, 1, 15, 20, 13, 14, 1, 22, 17, 14, 1, 54, 1, 16, 15, 26, 1, 20, 1, 28, 21, 18, 1, 30, 17, 16, 23, 32, 1, 60, 1, 34, 17, 1, 19, 78, 1, 22, 27, 74, 1, 18, 1, 40, 29, 24, 19, 90, 1, 22, 1, 44
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OFFSET

1,6


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537 (first 1000 terms from T. D. Noe)
C. Pomerance and H.S. Yang, Variant of a theorem of Erdős on the sumofproperdivisors function, Mathematics of Computation, to appear c. 2014


FORMULA

a(n) = sum (A077610(n,k): k = 1..A034444(n)1).  Reinhard Zumkeller, Aug 15 2012


EXAMPLE

Unitary divisors of 12 are 1, 3, 4, 12.


MAPLE

A034460 := proc(n)
A034448(n)n ;
end proc:
seq(A034460(n), n=1..40) ; # R. J. Mathar, Nov 10 2014


MATHEMATICA

usigma[n_] := Sum[ If[GCD[d, n/d] == 1, d, 0], {d, Divisors[n]}]; a[n_] := usigma[n]  n; Table[ a[n], {n, 1, 82}] (* JeanFrançois Alcover, May 15 2012 *)


PROG

(Haskell)
a034460 = sum . init . a077610_row  Reinhard Zumkeller, Aug 15 2012
(PARI) a(n)=sumdivmult(n, d, if(gcd(d, n/d)==1, d))n \\ Charles R Greathouse IV, Aug 01 2016


CROSSREFS

Cf. A034444, A034448.
Cf. A063936 (squares > 1).
Cf. A063919 (essentially the same sequence).
Sequence in context: A064793 A275109 A320832 * A063919 A308135 A072815
Adjacent sequences: A034457 A034458 A034459 * A034461 A034462 A034463


KEYWORD

nonn,easy,nice


AUTHOR

N. J. A. Sloane


STATUS

approved



