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A140826 Arithmetic nondivisor means.

%I A140826 #24 Sep 30 2024 04:49:17
%S A140826 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 A140826 79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,
%U A140826 173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269
%N A140826 Arithmetic nondivisor means.
%C A140826 Numbers n such that A024816(n)/(n-A000005(n)) is an integer.
%C A140826 Numbers n such that A231167(n) = 0. - _Jaroslav Krizek_, Nov 07 2013
%C A140826 Union of odd primes (A065091) and composites from A230605 (4, 18, 20, 24, 432, 588...). - _Jaroslav Krizek_, Nov 07 2013
%H A140826 Robert Israel, <a href="/A140826/b140826.txt">Table of n, a(n) for n = 1..10000</a>
%F A140826 Numbers n such that (n*n+n-2*A000203(n))/(2*n-2*A000005(n)) is an integer.
%e A140826 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 A140826 antisigma_1(18) = 4+5+7+8+10+11+12+13+14+15+16+17 = 132.
%e A140826 antisigma_0(18) = 12.
%e A140826 132/12 = 11 which is an integer so n=18 belongs to the sequence.
%p A140826 A024816 := proc(n) n*(n+1)/2-numtheory[sigma](n) ; end:
%p A140826 isA140826 := proc(n) if A024816(n) mod ( n-A000005(n)) = 0 then true; else false; fi; end:
%p A140826 for n from 3 to 400 do if isA140826(n) then printf("%d,",n) ; fi; od: # _R. J. Mathar_, Dec 13 2008
%t A140826 Select[Range[3, 300], IntegerQ[(#^2 + # - 2 DivisorSigma[1, #])/(2# - 2 DivisorSigma[0, #])]&] (* _Jean-François Alcover_, May 11 2023 *)
%o A140826 (PARI) isok(n) = (nnd = n - numdiv(n)) && !((n*(n+1)/2-sigma(n)) % nnd); \\ _Michel Marcus_, Nov 09 2013
%Y A140826 Cf. A000005, A003601, A024816, A049820, A000203.
%K A140826 easy,nonn
%O A140826 1,1
%A A140826 _Ctibor O. Zizka_, Jul 17 2008
%E A140826 Inserted 20 and extended by _R. J. Mathar_, Dec 13 2008