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Anti-Chowla's function: sum of anti-divisors of n except the largest.
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%I #41 May 13 2013 01:54:22

%S 0,0,0,0,2,0,5,3,2,7,5,5,10,7,8,3,17,16,5,11,8,21,19,7,22,7,24,27,5,

%T 16,21,37,26,7,29,8,25,45,26,28,14,38,27,11,56,27,29,24,39,47,8,59,53,

%U 16,37,19,36,57,51,67,16,37,70,3,41,42,87,67,8,55

%N Anti-Chowla's function: sum of anti-divisors of n except the largest.

%C Numbers n such that Chowla's function(n) = a(n): 1, 2, 3, 10, 15, 28, 75, 88, 231, 284, 602,...

%C Places n where a(n) is zero: 1, 2, 3, 4, 6, 96,...

%C Fixed points of this sequence: 17, 53, 127, 217, 385, 2321,...

%C Places n where a(n) equals the largest anti-divisor: 1, 2, 7, 10, 31, 37, 39, 55, 78, 160, 482, 937, 1599, 2496,...

%C Numbers n such that n -/+ 1 and a(n -/+ 1) are all primes: 6, 18, 72, 102, 108, 198, 270, 432, 570, 882,...

%H Charles R Greathouse IV, <a href="/A216982/b216982.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A066417(n) - A066481(n).

%e Anti-divisors of 7 are 2, 3, 5, so a(7) = 2 + 3 = 5.

%p A216982 := proc(n)

%p A066417(n)-A066481(n) ;

%p end proc: # _R. J. Mathar_, Feb 23 2013

%o (PARI) a(n)=if(n<5,0,my(k=valuation(n, 2)); sigma(2*n+1)+sigma(2*n-1)+sigma(n>>k)<<(k+1)-2-20*n\/3) \\ _Charles R Greathouse IV_, Mar 05 2013

%Y Cf. A048050, A066272, A066417, A066481, A130799, A218767.

%K nonn

%O 1,5

%A _Juri-Stepan Gerasimov_, Feb 19 2013