what is most special about a given integer?

[N. J. A. Sloane]

My colleague Edgar Gilbert was always interested
in such questions.

See A058974 for an interesting property of 38:


%I A058974
%S A058974 0,0,0,2,0,5,0,2,3,7,0,5,0,12,10,2,0,5,0,7,17,13,0,5,5,25,3,12,
%T A058974 0,17,0,2,26,19,17,5,0,38,18,7,0,17,0,13,10,30,0,5,7,7,27,25,0,
%U A058974 5,18,12,35,31,0,17,0,59,17,2,23,18,0,19,51,26,0,5,0,57,10,38,23
%N A058974 a(n) = 0 if n = 1 or a prime, otherwise a(n) = s + a(s), where s (A008472) is sum of distinct primes dividing n.
%D A058974 E. N. Gilbert, An interesting property of 38, unpublished, circa 1992. Shows that 38 is the only solution of a(n) = n.
%O A058974 1,4
%K A058974 nonn
%p A058974 f:=proc(n) option remember; local t1,i; if n=1 then RETURN(0) else t1:=0; for i from 1 to n do if n mod ithprime(i) = 0 then t1:=t1+ithprime(i); fi; od; fi; t1; end; A058974:=proc(n) local s; if n=1 then RETURN(0); fi; if isprime(n) then RETURN
%A A058974 njas, Jan 15 2001

njas