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

39, 119, 253, 581, 1875, 2077, 14477, 15879, 17823, 100637, 160529, 232477, 251189, 286437, 506587, 552739, 605729, 806179, 1170695, 3272257, 3295289, 4085129, 4201441, 4657133, 4844701, 5625173, 8106509, 12430289, 23943721, 33857009, 41782973, 64012513

Offset: 1

Author

Paolo P. Lava, Mar 21 2014

Keywords

• nonn
• base
• hard

Examples

			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.
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.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..65 (terms < 3*10^9)

Crossrefs

Cf. A000203, A239563.

Programs

Maple

with(numtheory);
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:=proc(q) local a,b,c,d,i,n; for n from 1 to q do a:=sigma(n); b:=T(n);
for i from 1 to b-1 do c:=trunc(n/10^i); d:=n-c*10^i;
if sigma(c)+sigma(d)=a-n then print(n); break; fi;  od; od; end: P(10^9);

Extensions

a(19)-a(32) from Giovanni Resta, Mar 21 2014