A375574 Let d(1)

1, 6, 6, 28, 28, 24, 126, 234, 224, 360, 504, 980, 990, 1260, 1764, 1680, 840, 1080, 4140, 960, 5760, 4620, 9180, 11088, 8960, 6120, 11880, 25740, 7140, 2520, 2016, 25344, 9720, 48672, 11760, 10920, 15120, 14112, 61740, 55200, 74340, 91800, 8190, 78624, 70200

Offset: 1

Author

Michel Lagneau, Aug 19 2024

Keywords

• nonn

Comments

The index i of s among the divisors of k is i = A375593(n), i.e. s = d(A375593(n)).

Examples

			*----*------*---------*---------------------------------*
| n  | a(n) |  i |  i-th   |  sum of n first divisors   |
|    |      |    | divisor |         of a(n)            |
*----*------*---------*---------------------------------*
| 2  |   6  |  3 |    3    | 1+2 = 3                    |
*----*------*----*---------*----------------------------*
| 3  |   6  |  4 |    6    | 1+2+3 = 6                  |
*----*------*----*---------*----------------------------*
| 4  |  28  |  5 |   14    | 1+2+4+7 = 14               |
*----*------*----*---------*----------------------------*
| 5  |  28  |  6 |   28    | 1+2+4+7+14 = 28            |
*----*------*----*---------*----------------------------*
| 6  |  24  |  8 |   24    | 1+2+3+4+6+8 = 24           |
*----*------*----*---------*----------------------------*
| 7  | 126  | 10 |   42    | 1+2+3+6+7+9+14 = 42        |
*----*------*----*---------*----------------------------*
| 8  | 234  | 10 |   78    | 1+2+3+6+9+13+18+26 = 78    |
*----*------*----*---------*----------------------------*
| 9  | 224  | 11 |  112    | 1+2+4+7+8+14+16+28+32 = 112|
|----*------*----*---------*----------------------------*
		

Links

• David A. Corneth, PARI program

Crossrefs

Cf. A000005, A000203, A001065, A240698, A375593.

Programs

Maple

with(numtheory):nn:=10^6:T:=array(1..44):i:=0:
for n from 2 to 45 do:
 ii:=1:
  for a from 6 to nn while ii=1
do:
    d:=divisors(a):n0:=nops(d):
     if n0>=n
      then
       s:=sum('d[j]', 'j'=1..n):
       for m from 1 to n0 do:
        if s=d[m]
         then
          ii:=0:printf(`%d %d\n`,n,a):i:=i+1:T[i]:=a:
           else
          fi :
        od :fi:
  od:od:print(T):

PARI

\\ See Corneth link

Python

from sympy import divisors
from itertools import count, islice
def agen(): # generator of terms
    adict, n = dict(), 1
    for k in count(1):
        d = divisors(k)
        if len(d) < n-1: continue
        dset, s = set(d), 0
        for i, di in enumerate(d, 1):
            s += di
            if i >= n and i not in adict and s in dset: adict[i] = k
        while n in adict: yield adict[n]; n += 1
print(list(islice(agen(), 50))) # Michael S. Branicky, Aug 20 2024

Extensions

a(1) = 1 prepended by David A. Corneth, Aug 20 2024