A289776 - OEIS

%I #25 Sep 16 2017 03:15:56

%S 2,4,30,16,84,36,60,144,144,144,144,210,324,360,630,756,756,576,660,

%T 840,840,2040,900,900,2304,1980,1980,1980,4320,5184,3300,4620,5460,

%U 7056,3960,4680,2520,3600,3600,3600,10080,8100,3600,6300,9900,7920,11088,14400

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

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

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

%H Chai Wah Wu, <a href="/A289776/b289776.txt">Table of n, a(n) for n = 2..1000</a>

%e 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.

%p with(numtheory):nn:=10^6:

%p for n from 2 to 50 do:

%p ii:=0:

%p    for k from 2 to nn while(ii=0) do:

%p      x:=divisors(k):n0:=nops(x):

%p        for l from 1 to n0 while(ii=0) do:

%p         p:=sum('x[i]', 'i'=1..l):

%p         if type(p,prime)=true and l=n

%p          then

%p          ii:=1:printf (`%d %d \n`,n,k):

%p          else fi:

%p         od:

%p       od:

%p   od:

%t 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 *)

%o (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

%o (Python)

%o from sympy import divisors, isprime

%o def A289776(n):

%o     i = 1

%o     while len(divisors(i)) < n or not isprime(sum(divisors(i)[:n])):

%o         i += 1

%o     return i # _Chai Wah Wu_, Aug 05 2017

%Y Cf. A000040, A027750, A240698.

%K nonn

%O 2,1

%A _Michel Lagneau_, Jul 12 2017