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A289776
Least k such that the sum of the first n divisors of k is a prime number.
5
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, ...
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
KEYWORD
nonn
AUTHOR
Michel Lagneau, Jul 12 2017
STATUS
approved