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%I #27 Sep 08 2022 08:45:34
%S 6,56,57,124,136,148,176,305,352,645,1016,2465,19305,61132,162525,
%T 476672,567645,712725,801945,2435489,3346400,3885057,4556000,8085561,
%U 8369361,12516693,22702120,29628801,83884032,83994625,84789248,354812536,860616296
%N Numbers n such that phi(n)*sigma(n)=phi(n-1)*sigma(n-1) (phi is the Euler totient function A000010 and sigma is the sum-of-divisors function A000203).
%C Up to 5*10^12 only n=696004 satisfies the similar relation phi(n)/sigma(n)=phi(n-1)/sigma(n-1), or equivalently, phi(n)sigma(n-1)=phi(n-1)/sigma(n). - _Giovanni Resta_, Aug 05 2013
%D J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 136, pp 46, Ellipses, Paris 2008.
%H Giovanni Resta, <a href="/A140790/b140790.txt">Table of n, a(n) for n = 1..52</a> (terms < 10^13)
%H K. Matthews, <a href="http://www.numbertheory.org/php/factor.html">Factorizing n and calculating phi(n),omega(n),d(n),sigma(n) and mu(n)</a>
%e 124 is in the sequence because phi(124)*sigma(124) = 60*224 = 13440 and phi(123)*sigma(123) = 80*168 = 13440, so that we indeed have phi(124)*sigma(124) = phi(123)*sigma(123).
%p lastv:= 0: A:= NULL:
%p for n from 1 to 10^7 do
%p v:= numtheory:-phi(n)*numtheory:-sigma(n);
%p if v = lastv then A:= A,n fi;
%p lastv:= v;
%p od:
%p A; # _Robert Israel_, Feb 04 2018
%t Select[Range[10^7], EulerPhi[#]DivisorSigma[1, #] == EulerPhi[# - 1] DivisorSigma[1, # - 1] &] (* _Vincenzo Librandi_, Feb 05 2018 *)
%o (PARI) isok(n) = (eulerphi(n)*sigma(n) == eulerphi(n-1)*sigma(n-1)) \\ _Michel Marcus_, Jul 28 2013
%o (Magma) [n: n in [2..10^6] | (EulerPhi(n)*SumOfDivisors(n) eq EulerPhi(n-1)*SumOfDivisors(n-1))]; // _Vincenzo Librandi_, Feb 05 2018
%K nonn
%O 1,1
%A _Lekraj Beedassy_, Jul 14 2008
%E a(29)-a(33) from _Donovan Johnson_, Jul 25 2011
%E Duplicated entry (19305) deleted by _Giovanni Resta_, Aug 05 2013
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