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A260097 Numbers n = concat(s,t) such that n = sigma(s*t), where sigma(x) is the sum of the divisors of x.

%I A260097 #29 Dec 18 2024 19:08:04
%S A260097 124,2352,2604,6804,15240,63180,225302,632400,1531152,2537040,4592588,
%T A260097 7160400,7603680,26100144,26378352,31492032,33747840,49447728,
%U A260097 88385040,104941200,162496048,175600040,197499456,403242624,483741216,797091840,2077442640,2942021520,4045874976,4828299840
%N A260097 Numbers n = concat(s,t) such that n = sigma(s*t), where sigma(x) is the sum of the divisors of x.
%e A260097 124 = concat(12,4) and sigma(12*4) = sigma(48) = 124.
%e A260097 2352 = concat(23,52) and sigma(23*52) = sigma(1196) = 2352.
%p A260097 with(numtheory); P:=proc(q) local a,b,i,n,p; for n from 1 to q do
%p A260097 for i from 1 to ilog10(n) do a:=trunc(n/10^i); b:=n-a*10^i;
%p A260097 if sigma(a*b)=n then print(n); break; fi; od; od; end: P(10^9);
%o A260097 (PARI) isok(n) = {len = #Str(n); for (k=1, len-1, na = n\10^k; nb = n % 10^k; if (nb && (n == sigma(na*nb)), return (1)); ); } \\ _Michel Marcus_, Jul 17 2015
%o A260097 (Python)
%o A260097 from sympy import divisor_sigma
%o A260097 A260097_list= []
%o A260097 for n in range(11,10**6):
%o A260097     s = str(n)
%o A260097     for l in range(1, len(s)):
%o A260097         m = int(s[:l])*int(s[l:])
%o A260097         if m > 0 and n == divisor_sigma(m):
%o A260097             A260097_list.append(n)
%o A260097             break # _Chai Wah Wu_, Jul 18 2015
%Y A260097 Cf. A000203, A253824, A253825.
%K A260097 nonn,base
%O A260097 1,1
%A A260097 _Paolo P. Lava_, Jul 16 2015
%E A260097 a(14)-a(15) from _Chai Wah Wu_, Jul 18 2015
%E A260097 a(16)-a(28) from _Lars Blomberg_, Jul 21 2015
%E A260097 a(29)-a(30) from _Giovanni Resta_, Jul 24 2015