A320518 - OEIS

%I #18 Jul 18 2020 04:32:50

%S 5,11,19,23,29,41,47,53,59,79,83,89,101,103,107,113,131,137,139,149,

%T 167,173,179,191,197,223,227,233,239,251,257,263,269,271,281,293,307,

%U 311,317,347,349,353,359,367,379,383,389,401,419,431,439,443,461,463

%N Zumkeller primes: k is prime and k + 1 is Zumkeller.

%H Amiram Eldar, <a href="/A320518/b320518.txt">Table of n, a(n) for n = 1..10000</a>

%p isZumkellerPrime := n -> isprime(n) and isZumkeller(n+1):

%p A320518_list := upto -> select(isZumkellerPrime, [$1..upto]): A320518_list(500);

%t ZumkellerQ[n_] := Module[{d = Divisors[n], ds, x}, ds = Total[d]; If[OddQ[ds], False, SeriesCoefficient[Product[1 + x^i, {i, d}], {x, 0, ds/2}] > 0]];

%t Select[Prime[Range[100]], ZumkellerQ[# + 1]&] (* _Jean-François Alcover_, Mar 01 2019 *)

%Y Cf. A083207, A000040.

%K nonn

%O 1,1

%A _Peter Luschny_, Oct 14 2018