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A259932 Primes whose anti-divisors sum to a prime.

%I A259932 #18 Jul 10 2015 08:45:23
%S A259932 3,5,13,41,113,761,1201,1741,1861,2113,9661,9941,12641,13613,15313,
%T A259932 21841,23981,30013,34061,47741,49613,60901,70313,83641,101701,237361,
%U A259932 241513,252761,303421,335381,377581,413141,489061,491041,525313,529421,637321,695021,718801
%N A259932 Primes whose anti-divisors sum to a prime.
%C A259932 See A066272 for definition of anti-divisor.
%C A259932 Subsequence of A109350.
%C A259932 Apparently, apart from 5, all terms are congruent to {1, 3} mod 5 (see A045429).
%H A259932 Paolo P. Lava, <a href="/A259932/b259932.txt">Table of n, a(n) for n = 1..100</a>
%e A259932 The anti-divisor of 3 is 2, which is prime.
%e A259932 The anti-divisors of 41 are 2, 3, 9, and 27, whose sum is 41, which is prime.
%e A259932 The anti-divisors of 9941 are 2, 3, 9, 47, 59, 141, 337, 423, 2209, and 6627, whose sum is 9857, which is prime.
%p A259932 with(numtheory): P:=proc(q) local a,i,j,n;
%p A259932 for n from 3 to q do if isprime(n) then
%p A259932 i:=0; j:=n; while j mod 2 <> 1 do i:=i+1; j:=j/2; od;
%p A259932 if isprime(sigma(2*n+1)+sigma(2*n-1)+sigma(n/2^i)*2^(i+1)-6*n-2)
%p A259932 then print(n); fi; fi; od; end: P(10^9);
%t A259932 ad[n_] := Cases[Range[2, n - 1], _?(Abs[Mod[n, #] - #/2] < 1 &)]; Select[Prime@ Range@ 1250, PrimeQ[Total@ ad@ #] &] (* _Michael De Vlieger_, Jul 10 2015 *)
%Y A259932 Cf. A000040, A045429, A066272, A066417, A109350.
%K A259932 nonn
%O A259932 1,1
%A A259932 _Paolo P. Lava_, Jul 09 2015