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Numbers n such that sigma(phi(n)) = sigma(n) - phi(n).
2

%I #12 Apr 27 2016 16:31:36

%S 172,248,765,4712,8924,16898,28552,50692,99302,229845,279490,280456,

%T 292995,300430,323488,334990,338990,346318,376790,403790,521738,

%U 548504,617918,1445824,1625806,2642596,2967724,3935764,7878836,8751946,8810865,9346790,11741128

%N Numbers n such that sigma(phi(n)) = sigma(n) - phi(n).

%C Tested up to n = 10^6.

%H Donovan Johnson, <a href="/A230371/b230371.txt">Table of n, a(n) for n = 1..228</a> (terms < 3*10^10)

%e phi(172) = 84, sigma(172) = 308, sigma(84) = 224 and 308 - 84 = 224.

%p with(numtheory);P:=proc(q) local n;

%p for n from 1 to q do

%p if sigma(phi(n))=sigma(n)-phi(n) then print(n);

%p fi; od; end: P(10^6);

%t dpQ[n_]:=Module[{p=EulerPhi[n]},DivisorSigma[1,p]==DivisorSigma[1,n]-p]; Select[Range[12*10^6],dpQ] (* _Harvey P. Dale_, Apr 27 2016 *)

%Y Cf. A000010, A000203, A062402, A230023, A230372.

%K nonn

%O 1,1

%A _Paolo P. Lava_, Oct 17 2013