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 A034460 a(n) = usigma(n) - n, where usigma(n) = sum of unitary divisors of n (A034448). 50
 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: A275109 A331735 A320832 * A063919 A308135 A072815 Adjacent sequences:  A034457 A034458 A034459 * A034461 A034462 A034463 KEYWORD nonn,easy,nice AUTHOR STATUS approved

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Last modified April 15 06:12 EDT 2021. Contains 342975 sequences. (Running on oeis4.)