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A260108 Primes of the form sigma(n) + product of divisors of n. 1
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 (list; graph; refs; listen; history; text; internal format)
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 A088823

Adjacent sequences:  A260105 A260106 A260107 * A260109 A260110 A260111

KEYWORD

nonn

AUTHOR

K. D. Bajpai, Jul 16 2015

STATUS

approved

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Last modified January 29 03:07 EST 2022. Contains 350672 sequences. (Running on oeis4.)