%I #24 Sep 22 2024 17:35:05

%S 1,3,4,5,7,11,13,17,19,23,29,31,36,37,41,43,47,53,59,61,67,71,73,79,

%T 83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,

%U 179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263

%N Numbers n such that antisigma(n) mod n = n - 1.

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

%C Union of A065091 (odd primes) and sequence nonprimes 1, 4, 36, ... (all terms < 10^5).

%C No more composite terms to 10^10. - _Charles R Greathouse IV_, Nov 02 2014

%H Jaroslav Krizek, <a href="/A227231/b227231.txt">Table of n, a(n) for n = 1..5000.</a>

%e antisigma(36) mod 36 => 575 mod 36 = 35.

%o (Magma) [n: n in [1..1000] | n-1 eq ((n*(n+1) div 2-SumOfDivisors(n)) mod n)]; // _Jaroslav Krizek_, May 28 2014

%o (PARI) is(n)=(n*(n+1)/2-sigma(n)+1)%n==0 \\ _Charles R Greathouse IV_, Nov 02 2014

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

%K nonn,changed

%O 1,2

%A _Jaroslav Krizek_, Sep 26 2013