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Integers m such that phi(m) is equal to the sum of (the product of prime factors) and (the product of exponents) of m-1.
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%I #28 Jul 28 2024 10:45:12

%S 2,5,21,45,285,765,27645,196605,41067645,72787965,250871805,

%T 4295098365,12884901885,23307153405,172130669565,1766029428523005,

%U 20978888016396285

%N Integers m such that phi(m) is equal to the sum of (the product of prime factors) and (the product of exponents) of m-1.

%C No other terms below 10^24. Some large terms: 1039619980803100740810795122685, 32576974833437288924302842789885. - _Max Alekseyev_, Jul 28 2024

%C All listed terms represent solutions to phi(m) = (m+3)/2 such that (m-1)/2 is an even squarefree number. Cf. A350777. - _Max Alekseyev_, Jul 21 2024

%C a(1)=2 is the only even term below 10^100000. - _Max Alekseyev_, Jul 22 2024

%e 21 is a term since 21-1 = 2^2*5^1 and (2*5)+(2*1) = 12 = phi(21).

%Y Cf. A000010, A039696, A350777.

%K nonn,more,hard

%O 1,1

%A _Olivier GĂ©rard_

%E More terms from _Jud McCranie_

%E Corrected example and a(11)-a(14) from _Donovan Johnson_, Nov 14 2010

%E a(15)-a(17) from _Max Alekseyev_, Jul 21 2024