cp's OEIS Frontend

A260108 Primes of the form sigma(k) + product of divisors of k.

%I A260108 #15 Jun 04 2025 14:00:50
%S A260108 2,5,7,11,79,23,47,769,59,32831,83,125093,107,3329,167,7333,179,12473,
%T A260108 227,268435711,263,26113,347,359,383,46489,467,56489,479,14706467,503,
%U A260108 70549,20797247,563,587,102121,126457,719,133669,153313,171049,839,863,191449,887
%N A260108 Primes of the form sigma(k) + product of divisors of k.
%C A260108 Alternatively: Primes arising in A259973.
%H A260108 K. D. Bajpai, <a href="/A260108/b260108.txt">Table of n, a(n) for n = 1..10000</a>
%e A260108 a(5) = 79; divisors(8) = {1,2,4,8}; sum = 1+2+4+8 = 15; product = 1*2*4*8 = 64; 15 + 64 = 79 which is prime.
%e A260108 a(8) = 769; divisors(27) = {1,3,9,27}; sum = 1+3+9+27 = 40; product = 1*3*9*27 = 729; 40+729 = 769 which is prime.
%p A260108 with(numtheory): A260108:= n-> (sigma(n) + convert( divisors(n), `*`)): select(isprime, [seq((A260108 (n), n=1..800))]);
%t A260108 Select[Table[DivisorSigma[1, n] + Times @@ Divisors[n], {n, 1, 1000}], PrimeQ]
%o A260108 (PARI) for(n=1, 1000, d=divisors(n); k=sigma(n) + prod(i=1, #d, d[i]); if( isprime(k) , print1(k, ", ")));
%o A260108 (PARI) A007955(n)=if(issquare(n, &n), n^numdiv(n^2), n^(numdiv(n)/2))
%o A260108 list(lim)=v=List([2]); forprime(p=2,(lim-1)\2, if(isprime(2*p+1), listput(v,2*p+1))); forprime(p=2,sqrtnint(lim\1,3), my(t=p^3+p^2+p+1); if(t>lim,break); if(isprime(t), listput(v,t))); forcomposite(n=4,sqrtint(lim\1), my(t=A007955(n)+sigma(n)); if(t<=lim && isprime(t), listput(v,t))); Set(v) \\ _Charles R Greathouse IV_, Jul 17 2015
%o A260108 (Magma) [k: n in[1..1000] | IsPrime(k) where k is (&*Divisors(n) + SumOfDivisors(n))];
%Y A260108 Cf. A000203, A007955, A065512, A118369, A259973.
%K A260108 nonn
%O A260108 1,1
%A A260108 _K. D. Bajpai_, Jul 16 2015