A375593 Index i among the divisors of k = A375574(n) of the sum s of the first n divisors of k.

1, 3, 4, 5, 6, 8, 10, 10, 11, 19, 20, 16, 20, 28, 22, 32, 29, 29, 29, 27, 38, 40, 39, 47, 33, 42, 52, 55, 43, 46, 36, 47, 45, 47, 54, 58, 70, 51, 59, 62, 60, 77, 48, 80, 82, 75, 67, 79, 67, 68, 80, 84, 91, 62, 107, 98, 99, 88, 112, 103, 120, 70, 96, 88, 89, 72, 98

Offset

1,2

Comments

k = A375574(n) is the smallest k for which such sum s is a divisor of k.

Links

Table of n, a(n) for n=1..67.

Example

a(24) = 47 because the sum of the 24 first divisors of k = A375574(24) = 11088 is s = 1+2+3+4+6+7+8+9+11+12+14+16+18+21+22+24+28+33+36+42+44+48+56+63 = 528 which is the 47th divisor of 11088.

Maple

with(numtheory):nn:=10^7:T:=array(1..79):i:=0:
for n from 2 to 80 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 %d\n`, n, a, m):i:=i+1:T[i]:=m:
           else
          fi :
        od :fi:
  od:od:print(T):

Prog

(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] = d.index(s) + 1
        while n in adict: yield adict[n]; n += 1
print(list(islice(agen(), 65))) # Michael S. Branicky, Aug 20 2024

Crossrefs

Cf. A375574.

Sequence in context: A299114 A376608 A103605 * A098171 A039031 A047309

Adjacent sequences: A375590 A375591 A375592 * A375594 A375595 A375596

Keyword

nonn

Author

Michel Lagneau, Aug 20 2024

Status

approved