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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 (list; graph; refs; listen; history; text; internal format)
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 sum-of-proper-divisors 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}] (* Jean-François 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

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Last modified December 7 09:33 EST 2019. Contains 329843 sequences. (Running on oeis4.)