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A297365 Numbers n such that uphi(n)*usigma(n) = uphi(n+1)*usigma(n+1), where uphi is the unitary totient function (A047994) and usigma the sum of unitary divisors (A034448). 0

%I

%S 5,11,19,71,247,271,991,2232,6200,8271,10295,16744,18496,18576,25704,

%T 26656,102175,122607,166624,225939,301103,747967,7237384,7302592,

%U 15760224,21770800,28121184,72967087,98617024,104577848,173859007,253496176,335610184,371191600

%N Numbers n such that uphi(n)*usigma(n) = uphi(n+1)*usigma(n+1), where uphi is the unitary totient function (A047994) and usigma the sum of unitary divisors (A034448).

%C The unitary version of A244439.

%e 11 is in the sequence since uphi(11) * usigma(11) = 10 * 12 = uphi(12) * usigma(12) = 6 * 20 = 120.

%t usigma[n_] := If[n == 1, 1, Times @@ (1 + Power @@@ FactorInteger[n])];

%t uphi[n_] := (Times @@ (Table[#[[1]]^#[[2]] - 1, {1}] & /@ FactorInteger[n]))[[1]]; u[n_] := uphi[n]*usigma[n]; aQ[n_] := u[n] == u[n + 1]; Select[Range[10^6], aQ]

%Y Cf. A034448, A047994, A244439.

%K nonn

%O 1,1

%A _Amiram Eldar_, Dec 29 2017

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Last modified April 10 08:09 EDT 2021. Contains 342845 sequences. (Running on oeis4.)