A097646 Numbers n such that n = phi(phi(n) + sigma(n)).

1, 2, 6, 10, 20, 22, 46, 48, 58, 82, 106, 166, 178, 180, 208, 226, 262, 346, 358, 382, 466, 478, 502, 562, 586, 718, 838, 862, 864, 886, 982, 1018, 1120, 1186, 1282, 1306, 1318, 1366, 1368, 1438, 1486, 1522, 1618, 1822, 1906, 2026, 2038, 2062, 2098, 2206

Offset: 1

Author

Farideh Firoozbakht, Sep 08 2004

Keywords

• nonn

Comments

If n=2*p where p is a Sophie Germain odd prime, then n is in the sequence; the proof is obvious.

Examples

			22 is in the sequence because phi(22)=10, sigma(22)=36 and phi(10+36)=22.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..10000
• C. K. Caldwell, The Prime Glossary, Sophie Germain prime.

Crossrefs

Cf. A077080, A097652, A005384, A097645, A018784.

Programs

Magma

[n: n in [1..2300] | n eq EulerPhi(EulerPhi(n) + DivisorSigma(1,n))]; // Vincenzo Librandi, Aug 22 2015

Maple

with(numtheory):K:=proc()local n,a,c;  c:=1; for n from 1 to 5000000 do;
a:=phi(phi(n)+ sigma(n));if  a=n  then lprint(c,n); c:=c+1; fi;od; end:K(); # K. D. Bajpai, Jul 18 2013

Mathematica

Do[If[n==EulerPhi[EulerPhi[n]+DivisorSigma[1, n]], Print[n]], {n, 2400}]
Select[Range[2500],EulerPhi[EulerPhi[#]+DivisorSigma[1,#]]==#&] (* Harvey P. Dale, Jul 06 2021 *)

PARI

is(n)=sigma(n=factor(n))==eulerphi(eulerphi(n)) \\ Charles R Greathouse IV, Nov 27 2013