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A140826 Arithmetic nondivisor means. 5

%I

%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

%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

%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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Last modified April 26 08:53 EDT 2019. Contains 322472 sequences. (Running on oeis4.)