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A052396 (+2)-sigma perfect numbers: numbers k such that (+2)sigma(k) = 2*k, where (+2)sigma(k) = A107758(k). 2

%I

%S 2,4,8,16,32,63,64,128,256,512,1024,2048,4096,8192,16384,32768,34587,

%T 65536,131072,262144,524288,1048576,2097152,4194304,8388608,16777216,

%U 33554432,67108864,134217728,170271801,268435456,536870912,1073741824,2147483648,4294967296

%N (+2)-sigma perfect numbers: numbers k such that (+2)sigma(k) = 2*k, where (+2)sigma(k) = A107758(k).

%C 2^n is a term for all n>=1. - _Amiram Eldar_, Aug 26 2022

%e Factorizations: even examples: 2, 2^2, 2^3, 2^4,...; odd examples: a(6) = 3^2*7, a(17) = 3^4*7*61, a(30) = 3^6*7*61*547.

%t f[p_, e_] := 1 + (p^(e + 1) - 1)/(p - 1); s[n_] := Times @@ f @@@ FactorInteger[n]; s[1] = 1; Select[Range[5*10^6], s[#] == 2*# &] (* _Amiram Eldar_, Aug 26 2022 *)

%Y Cf. A000079, A107758.

%K nonn

%O 1,1

%A _Yasutoshi Kohmoto_ Mar 13 2000

%E Corrected by _Franklin T. Adams-Watters_, Oct 25 2006

%E a(30) corrected and a(31)-a(35) added by _Amiram Eldar_, Aug 26 2022

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Last modified October 6 05:47 EDT 2022. Contains 357261 sequences. (Running on oeis4.)