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Numbers k such that antisigma(k) mod k = antisigma(k+1) mod (k+1).
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%I #14 Jul 12 2021 02:10:47

%S 1,8,27,3115,3451,4725,10611,15951,20155,27643,74875,2767675,18390564,

%T 27923284,50293331,425018875,897002491,10561657872,15193530235,

%U 20939306635,40882585915,80585844499

%N Numbers k such that antisigma(k) mod k = antisigma(k+1) mod (k+1).

%C Antisigma(k) = A024816(k) = sum of numbers less than k which do not divide k.

%C Numbers k such that A229110(k) = A229110(k+1).

%C For k < 10^8, 2 is the only number such that sigma(k) mod k = sigma(k+1) mod (k+1).

%C a(23) > 10^11. - _Donovan Johnson_, Sep 27 2013

%e a(3) = 27 because antisigma(27) mod 27 = 338 mod 27 = antisigma(28) mod 28 = 350 mod 28 = 14.

%o (PARI) s=1; r=0; for(n=1, 10^9, n1=n+1; s=s+n1; r1=(s-sigma(n1))%n1; if(r==r1, print(n)); r=r1) /* _Donovan Johnson_, Sep 27 2013 */

%Y Cf. A024816 (antisigma(n)), A229110 (antisigma(n) mod n).

%K nonn,more

%O 1,2

%A _Jaroslav Krizek_, Sep 26 2013

%E a(12)-a(22) from _Donovan Johnson_, Sep 27 2013