A289776 Least k such that the sum of the first n divisors of k is a prime number.

2, 4, 30, 16, 84, 36, 60, 144, 144, 144, 144, 210, 324, 360, 630, 756, 756, 576, 660, 840, 840, 2040, 900, 900, 2304, 1980, 1980, 1980, 4320, 5184, 3300, 4620, 5460, 7056, 3960, 4680, 2520, 3600, 3600, 3600, 10080, 8100, 3600, 6300, 9900, 7920, 11088, 14400

Offset: 2

Author

Michel Lagneau, Jul 12 2017

Keywords

• nonn

Comments

The corresponding primes are 3, 7, 11, 31, 23, 37, 43, 61, 79, 103, 139, 191, 523, 167, 263, 347, 431, 787, 641, ...

The squares in the sequence are 4, 16, 36, 144, 324, 576, 900, 2304, 3600, 5184, 7056, 8100, 14400, ...

Examples

			a(4)=30 because the sum of the first 4 divisors of 30 is 1 + 2 + 3 + 5 = 11, which is prime, and there is no integer below 30 with this property.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 2..1000

Crossrefs

Cf. A000040, A027750, A240698.

Programs

Maple

with(numtheory):nn:=10^6:
for n from 2 to 50 do:
ii:=0:
   for k from 2 to nn while(ii=0) do:
     x:=divisors(k):n0:=nops(x):
       for l from 1 to n0 while(ii=0) do:
        p:=sum('x[i]', 'i'=1..l):
        if type(p,prime)=true and l=n
         then
         ii:=1:printf (`%d %d \n`,n,k):
         else fi:
        od:
      od:
  od:

Mathematica

Table[k = 1; While[Nand[Length@ # >= n, PrimeQ@ Total@ Take[PadRight[#, n], n]] &@ Divisors@ k, k++]; k, {n, 2, 49}] (* Michael De Vlieger, Jul 12 2017 *)

PARI

a(n) = k=1; while((d=divisors(k)) && ((#dMichel Marcus, Jul 12 2017

Python

from sympy import divisors, isprime
def A289776(n):
    i = 1
    while len(divisors(i)) < n or not isprime(sum(divisors(i)[:n])):
        i += 1
    return i # Chai Wah Wu, Aug 05 2017