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A270836 Numbers k such that sigma(k-1) - phi(k-1) = (3*k-5)/2.

%I A270836 #30 Mar 27 2025 21:31:59
%S A270836 3,5,9,11,17,33,65,129,231,257,513,1025,2049,4097,8193,16385,32769,
%T A270836 65537,119831,131073,262145,524289,1048577,2097153,4194305,8388609,
%U A270836 16777217,33554433,67108865,134217729,268435457,536870913,1073741825,2147483649,4294967297
%N A270836 Numbers k such that sigma(k-1) - phi(k-1) = (3*k-5)/2.
%C A270836 Numbers k such that A051612(k-1) = (3*k-5)/2.
%C A270836 Numbers of the form 2^k + 1 for k >= 1 from A000051 are terms.
%C A270836 Prime terms are in A270778.
%H A270836 Giovanni Resta, <a href="/A270836/b270836.txt">Table of n, a(n) for n = 1..46</a> (terms < 10^13)
%e A270836 17 is a term because sigma(16) - phi(16) = 31-8 = 23 = (3*17-5)/2.
%t A270836 Select[Range[10^6], 2 (DivisorSigma[1, # - 1] - EulerPhi[# - 1]) == 3 # - 5 &] (* _Michael De Vlieger_, Mar 24 2016 *)
%o A270836 (Magma) [n: n in[2..10^7] | 2*(SumOfDivisors(n-1) - EulerPhi(n-1)) eq 3*n-5];
%o A270836 (PARI) lista(nn) = {for(n=2, nn, if(sigma(n-1) - eulerphi(n-1) == (3*n-5)/2, print1(n, ", "))); } \\ _Altug Alkan_, Mar 23 2016
%Y A270836 Cf. A000010, A000051, A000203, A051612, A270778, A270837.
%K A270836 nonn
%O A270836 1,1
%A A270836 _Jaroslav Krizek_, Mar 23 2016
%E A270836 a(30)-a(32) from _Michel Marcus_, Apr 05 2016
%E A270836 a(33)-a(35) from _Giovanni Resta_, Apr 11 2016