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

%I A375593 #20 Sep 13 2024 07:44:17
%S A375593 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,
%T A375593 42,52,55,43,46,36,47,45,47,54,58,70,51,59,62,60,77,48,80,82,75,67,79,
%U A375593 67,68,80,84,91,62,107,98,99,88,112,103,120,70,96,88,89,72,98
%N A375593 Index i among the divisors of k = A375574(n) of the sum s of the first n divisors of k.
%C A375593 k = A375574(n) is the smallest k for which such sum s is a divisor of k.
%e A375593 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.
%p A375593 with(numtheory):nn:=10^7:T:=array(1..79):i:=0:
%p A375593 for n from 2 to 80 do:
%p A375593  ii:=1:
%p A375593   for a from 6 to nn while ii=1
%p A375593 do:
%p A375593     d:=divisors(a):n0:=nops(d):
%p A375593      if n0>=n
%p A375593       then
%p A375593        s:=sum('d[j]', 'j'=1..n):
%p A375593        for m from 1 to n0 do:
%p A375593         if s=d[m]
%p A375593          then
%p A375593           ii:=0:printf(`%d %d %d\n`,n,a,m):i:=i+1:T[i]:=m:
%p A375593            else
%p A375593           fi :
%p A375593         od :fi:
%p A375593   od:od:print(T):
%o A375593 (Python)
%o A375593 from sympy import divisors
%o A375593 from itertools import count, islice
%o A375593 def agen(): # generator of terms
%o A375593     adict, n = dict(), 1
%o A375593     for k in count(1):
%o A375593         d = divisors(k)
%o A375593         if len(d) < n-1: continue
%o A375593         dset, s = set(d), 0
%o A375593         for i, di in enumerate(d, 1):
%o A375593             s += di
%o A375593             if i >= n and i not in adict and s in dset:
%o A375593                 adict[i] = d.index(s) + 1
%o A375593         while n in adict: yield adict[n]; n += 1
%o A375593 print(list(islice(agen(), 65))) # _Michael S. Branicky_, Aug 20 2024
%Y A375593 Cf. A375574.
%K A375593 nonn
%O A375593 1,2
%A A375593 _Michel Lagneau_, Aug 20 2024