A290126 Least k such that the sum of the n greatest divisors of k is a prime number.

2, 2, 4, 28, 16, 140, 24, 90, 120, 108, 60, 144, 300, 288, 120, 672, 252, 432, 240, 630, 960, 756, 480, 1200, 1080, 1728, 1680, 1008, 720, 2016, 840, 3150, 2160, 2700, 1980, 4800, 2520, 3780, 3240, 8736, 3960, 3600, 6720, 6930, 10800, 6300, 4200, 16848, 9240, 5040

Offset: 1

Author

Michel Lagneau, Jul 20 2017

Keywords

• nonn

Comments

The corresponding primes are 2, 3, 7, 53, 31, 307, 59, 223, 331, 277, 167, 397, 853, 809, 359, 1973, 727, 1237, ...

The squares of the sequence are 4, 16, 144, 3600, ...

Examples

			a(4)=28 because the sum of the last 4 divisors of 28: 28+14+7+4 = 53 is a prime number.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000290, A027750, A240698, A289776.

Programs

Maple

M:= 20000: # to get all terms before the first term > M
R:= 'R':
for k from 2 to M do
   F:= ListTools:-PartialSums(sort(convert(
      numtheory:-divisors(k),list),`>`));
   for n in select(t -> isprime(F[t]),[$1..nops(F)]) do
    if not assigned(R[n]) then R[n]:= k fi
   od
od:
inds:= map(op,{indices(R)}):
N:= min({$1..max(inds)+1} minus inds):
seq(R[i],i=1..N-1);  # Robert Israel, Jul 24 2017

Mathematica

Table[k=1;While[Nand[Length@#>=n,PrimeQ[Total@Take[PadLeft[#,n],n]]]&@Divisors@k,k++];k,{n,1,20}](* Program from Michael De Vlieger adapted for this sequence. See A289776 *)

PARI

a(n) = {my(i = 2, d);  while(1, d = divisors(i); if(#d >= n, if(isprime(sum(j=#d-n+1,#d,d[j])), return(i), i++), i++)); i} \\ David A. Corneth, Jul 20 2017

Python

from sympy import divisors, isprime
def A290126(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