A260108 Primes of the form sigma(k) + product of divisors of k.
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
Keywords
Examples
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.
Links
- K. D. Bajpai, Table of n, a(n) for n = 1..10000
Programs
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Magma
[k: n in[1..1000] | IsPrime(k) where k is (&*Divisors(n) + SumOfDivisors(n))];
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Maple
with(numtheory): A260108:= n-> (sigma(n) + convert( divisors(n), `*`)): select(isprime, [seq((A260108 (n), n=1..800))]);
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Mathematica
Select[Table[DivisorSigma[1, n] + Times @@ Divisors[n], {n, 1, 1000}], PrimeQ] -
PARI
for(n=1, 1000, d=divisors(n); k=sigma(n) + prod(i=1, #d, d[i]); if( isprime(k) , print1(k, ", ")));
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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
Comments