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

1,1

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, ...

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A000290, A027750, A240698, A289776.

Sequence in context: A189870 A257614 A067068 * A266046 A032334 A032082

Adjacent sequences: A290123 A290124 A290125 * A290127 A290128 A290129

Keyword

nonn

Author

Michel Lagneau, Jul 20 2017

Status

approved