A272778 - OEIS

%I #14 May 10 2016 00:43:46

%S 48,1040,1196,2720,6080,19080,116644,252800,796172,1014800,2370352,

%T 2796800,2864000,12200288,13499120,13716716,15252992,21938672,

%U 33883520,43218800,62496048,70240000,98392832,129704960,199361792,318836720,548444160,1218624080

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

%H Giovanni Resta, <a href="/A272778/b272778.txt">Table of n, a(n) for n = 1..46</a> (terms < 2.5*10^11)

%e sigma(48) = 124 = concat(12,4) and 12 * 4 = 48;

%e sigma(1196) = 2352 = concat(23,52) = and 23 * 52 = 1196.

%p with(numtheory): P:=proc(q) local a, b, c, i, n;

%p for n from 1 to q do c:=sigma(n); for i from 1 to ilog10(c) do

%p a:=trunc(c/10^i);  b:=c-a*10^i; if a*b=n then print(n); break;

%p fi; od; od; end: P(10^9);

%t Select[Range[3*10^5], Function[n, Total@ Boole@ Function[k, n == First@ # Last@ # & /@ Map[FromDigits /@ TakeDrop[IntegerDigits@ k, #] &, Range[IntegerLength@ k - 1]]][DivisorSigma[1, n]] > 0]] (* _Michael De Vlieger_, May 07 2016, Version 10.2 *)

%Y Cf. A000203, A272779.

%K nonn,base

%O 1,1

%A _Paolo P. Lava_, May 06 2016

%E a(11)-a(28) from _Giovanni Resta_, May 06 2016