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

2,1

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, ...

Links

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

Example

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.

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 *)

Prog

(PARI) a(n) = k=1; while((d=divisors(k)) && ((#d<n) || !isprime(sum(j=1, n, d[j]))), k++); k; \\ Michel 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

Crossrefs

Cf. A000040, A027750, A240698.

Sequence in context: A081464 A216026 A241589 * A290169 A232173 A067195

Adjacent sequences: A289773 A289774 A289775 * A289777 A289778 A289779

Keyword

nonn

Author

Michel Lagneau, Jul 12 2017

Status

approved