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A239562 Numbers n such that n = concatenate(a, b) and sigma(a) + sigma(b) = sigma(n) - n. 5

%I

%S 39,119,253,581,1875,2077,14477,15879,17823,100637,160529,232477,

%T 251189,286437,506587,552739,605729,806179,1170695,3272257,3295289,

%U 4085129,4201441,4657133,4844701,5625173,8106509,12430289,23943721,33857009,41782973,64012513

%N Numbers n such that n = concatenate(a, b) and sigma(a) + sigma(b) = sigma(n) - n.

%H Giovanni Resta, <a href="/A239562/b239562.txt">Table of n, a(n) for n = 1..65</a> (terms < 3*10^9)

%e For n = 232477 we can consider 232477 = 2 U 32477 and sigma(232477) = 265696, sigma(2) = 3, sigma(32477) = 33216 and 265696 - 232477 = 33219 = 3 + 33216.

%e For n = 251189 we can consider 251189 = 25 U 1189 and sigma(251189) = 252480, sigma(25) = 31, sigma(1189) = 1260 and 252480 - 251189 = 1291 = 31 + 1260.

%p with(numtheory);

%p T:=proc(t) local w,x,y; x:=t; y:=0; while x>0 do x:=trunc(x/10); y:=y+1; od; end:

%p P:=proc(q) local a,b,c,d,i,n; for n from 1 to q do a:=sigma(n); b:=T(n);

%p for i from 1 to b-1 do c:=trunc(n/10^i); d:=n-c*10^i;

%p if sigma(c)+sigma(d)=a-n then print(n); break; fi; od; od; end: P(10^9);

%Y Cf. A000203, A239563.

%K nonn,base,hard

%O 1,1

%A _Paolo P. Lava_, Mar 21 2014

%E a(19)-a(32) from _Giovanni Resta_, Mar 21 2014

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Last modified May 28 15:33 EDT 2020. Contains 334684 sequences. (Running on oeis4.)