%I #13 Dec 02 2016 09:30:16
%S 1,19,126,162,231,255,717,1611,1897,3231,3735,8692,8774,10676,16903,
%T 17299,22194,30845,92049,309546,459780,502302,763755,788379
%N Numbers n such that the sum of the digits of sigma(n)^phi(n) is divisible by n.
%C No more terms < 58000. - _Emeric Deutsch_, Jul 25 2006
%e The digits of sigma(3735)^phi(3735) sum to 33615 and 33615 is divisible by 3735, so 3735 is in the sequence.
%p with(numtheory): sd:=proc(n) local nn: nn:=convert(n,base,10): add(nn[j],j=1..nops(nn)) end: a:=proc(n) if sd(sigma(n)^phi(n)) mod n = 0 then n else fi end: seq(a(n),n=1..2000); # _Emeric Deutsch_, Jul 25 2006
%t Do[s = DivisorSigma[1, n]^EulerPhi[n]; k = Plus @@ IntegerDigits[s]; If[Mod[k, n] == 0, Print[n]], {n, 1, 10^4}]
%t Select[Range[100000],Divisible[Total[IntegerDigits[DivisorSigma[1,#]^ EulerPhi[ #]]],#]&] (* _Harvey P. Dale_, Jan 03 2012 *)
%K base,more,nonn
%O 1,2
%A _Ryan Propper_, Aug 06 2005
%E More terms from _Emeric Deutsch_, Jul 25 2006
%E One more term (a(19)) from _Harvey P. Dale_, Jan 03 2012
%E a(20)-a(24) from _Lars Blomberg_, Dec 02 2016