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%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
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