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%I #20 May 11 2023 04:58:20
%S 3,4,5,7,11,13,17,18,19,20,23,24,29,31,37,41,43,47,53,59,61,67,71,73,
%T 79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,
%U 173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269
%N Arithmetic nondivisor means.
%C Numbers n such that a(n)=A024816(n)/(n-A000005(n)) is an integer.
%C Numbers n such that A231167(n) = 0. - _Jaroslav Krizek_, Nov 07 2013
%C Union of odd primes (A065091) and composites from A230605 (4, 18, 20, 24, 432, 588...). - _Jaroslav Krizek_, Nov 07 2013
%H Robert Israel, <a href="/A140826/b140826.txt">Table of n, a(n) for n = 1..10000</a>
%F Numbers n such that (n*n+n-2*A000203(n))/(2*n-2*A000005(n)) is an integer.
%e n=18: numbers less than n which do not divide n are 4,5,7,8,10,11,12,13,14,15,16,17.
%e antisigma_1(18) = 4+5+7+8+10+11+12+13+14+15+16+17) = 132
%e sigma_0(18) = 12
%e 132/12 = 11 which is an integer so n=18 belongs to the sequence.
%p A024816 := proc(n) n*(n+1)/2-numtheory[sigma](n) ; end:
%p isA140826 := proc(n) if A024816(n) mod ( n-A000005(n)) = 0 then true; else false; fi; end:
%p for n from 3 to 400 do if isA140826(n) then printf("%d,",n) ; fi; od: # _R. J. Mathar_, Dec 13 2008
%t Select[Range[3, 300], IntegerQ[(#^2 + # - 2 DivisorSigma[1, #])/(2# - 2 DivisorSigma[0, #])]&] (* _Jean-François Alcover_, May 11 2023 *)
%o (PARI) isok(n) = (nnd = n - numdiv(n)) && !((n*(n+1)/2-sigma(n)) % nnd); \\ _Michel Marcus_, Nov 09 2013
%Y Cf. A000005, A003601, A024816, A049820, A000203.
%K easy,nonn
%O 1,1
%A _Ctibor O. Zizka_, Jul 17 2008
%E Inserted 20 and extended by _R. J. Mathar_, Dec 13 2008
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