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%I #29 Jun 12 2018 21:14:44
%S 1,1,1,1,1,6,1,1,1,8,1,8,1,10,9,1,1,12,1,10,11,14,1,12,1,16,1,12,1,42,
%T 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,
%U 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
%N Sum of proper unitary divisors (or unitary aliquot parts) of n, including 1.
%C For definition of unitary divisor see A034448.
%H Antti Karttunen, <a href="/A063919/b063919.txt">Table of n, a(n) for n = 1..65537</a> (first 1000 terms from Harry J. Smith)
%F a(n) = A034460(n), n>1. - _R. J. Mathar_, Oct 02 2008
%F For n > 1: a(n) = sum (A077610(n,k): k = 1 .. A034444(n) - 1). - _Reinhard Zumkeller_, Mar 12 2012
%e a(10) = 8 because the unitary divisors of 10 are 1, 2, 5 and 10, with sum 18 and 18-10 = 8.
%p A063919 := proc(n)
%p if n = 1 then
%p 1;
%p else
%p A034448(n)-n ;
%p end if;
%p end proc: # _R. J. Mathar_, May 14 2013
%t a[n_] := Total[Select[Divisors[n], GCD[#, n/#] == 1&]]-n; a[1] = 1; Table[a[n], {n, 82}] (* _Jean-François Alcover_, Aug 31 2011 *)
%o (PARI) usigma(n) = sumdiv(n, d, if(gcd(d, n/d)==1, d))
%o { for (n=1, 1000, if (n>1, a=usigma(n) - n, a=1); write("b063919.txt", n, " ", a) ) } \\ _Harry J. Smith_, Sep 02 2009
%o (PARI)
%o A034460(n) = (sumdivmult(n, d, if(gcd(d, n/d)==1, d))-n); \\ From A034460
%o A063919(n) = if(1==n,n,A034460(n)); \\ _Antti Karttunen_, Jun 12 2018
%o (Haskell)
%o a063919 1 = 1
%o a063919 n = sum $ init $ a077610_row n
%o -- _Reinhard Zumkeller_, Mar 12 2012
%Y The values of sequence are A034448(n)-n (for n > 1).
%Y Cf. A001065, A034448, A034460.
%K easy,nonn,nice
%O 1,6
%A _Felice Russo_, Aug 31 2001
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