A259932 Primes whose anti-divisors sum to a prime.

3, 5, 13, 41, 113, 761, 1201, 1741, 1861, 2113, 9661, 9941, 12641, 13613, 15313, 21841, 23981, 30013, 34061, 47741, 49613, 60901, 70313, 83641, 101701, 237361, 241513, 252761, 303421, 335381, 377581, 413141, 489061, 491041, 525313, 529421, 637321, 695021, 718801

Offset: 1

Author

Paolo P. Lava, Jul 09 2015

Keywords

• nonn

Comments

See A066272 for definition of anti-divisor.

Subsequence of A109350.

Apparently, apart from 5, all terms are congruent to {1, 3} mod 5 (see A045429).

Examples

			The anti-divisor of 3 is 2, which is prime.
The anti-divisors of 41 are 2, 3, 9, and 27, whose sum is 41, which is prime.
The anti-divisors of 9941 are 2, 3, 9, 47, 59, 141, 337, 423, 2209, and 6627, whose sum is 9857, which is prime.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A000040, A045429, A066272, A066417, A109350.

Programs

Maple

with(numtheory): P:=proc(q) local a,i,j,n;
for n from 3 to q do if isprime(n) then
i:=0; j:=n; while j mod 2 <> 1 do i:=i+1; j:=j/2; od;
if isprime(sigma(2*n+1)+sigma(2*n-1)+sigma(n/2^i)*2^(i+1)-6*n-2)
then print(n); fi; fi; od; end: P(10^9);

Mathematica

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 *)