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

2, 5, 7, 11, 79, 23, 47, 769, 59, 32831, 83, 125093, 107, 3329, 167, 7333, 179, 12473, 227, 268435711, 263, 26113, 347, 359, 383, 46489, 467, 56489, 479, 14706467, 503, 70549, 20797247, 563, 587, 102121, 126457, 719, 133669, 153313, 171049, 839, 863, 191449, 887

Offset

1,1

Comments

Alternatively: Primes arising in A259973.

Links

K. D. Bajpai, Table of n, a(n) for n = 1..10000

Example

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.
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.

Maple

with(numtheory): A260108:= n-> (sigma(n) + convert( divisors(n), `*`)): select(isprime, [seq((A260108 (n), n=1..800))]);

Mathematica

Select[Table[DivisorSigma[1, n] + Times @@ Divisors[n], {n, 1, 1000}], PrimeQ]

Prog

(PARI) for(n=1, 1000, d=divisors(n); k=sigma(n) + prod(i=1, #d, d[i]); if( isprime(k) , print1(k, ", ")));
(PARI) A007955(n)=if(issquare(n, &n), n^numdiv(n^2), n^(numdiv(n)/2))
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
(Magma) [k: n in[1..1000] | IsPrime(k) where k is (&*Divisors(n) + SumOfDivisors(n))]

Crossrefs

Cf. A000203, A007955, A065512, A118369, A259973.

Sequence in context: A229209 A227613 A168031 * A265791 A039679 A374105

Adjacent sequences: A260105 A260106 A260107 * A260109 A260110 A260111

Keyword

nonn

Author

K. D. Bajpai, Jul 16 2015

Status

approved