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A270837 Numbers k such that sigma(k-1) + phi(k-1) = (5*k-7)/2.

%I A270837 #24 Mar 27 2025 19:14:44
%S A270837 3,5,7,9,17,33,65,67,129,257,513,1025,2049,4097,8193,16385,32769,
%T A270837 65537,131073,262145,524289,1048577,2097153,4194305,8388609,16777217,
%U A270837 33554433,67108865,134217729,268435457,536870913,1073741825,2147483649,4294967297,5606129563
%N A270837 Numbers k such that sigma(k-1) + phi(k-1) = (5*k-7)/2.
%C A270837 Numbers k such that A065387(k-1) = (5*k-7)/2.
%C A270837 Numbers of the form 2^k + 1 for k >= 1 from A000051 are terms.
%C A270837 Prime terms are in A270779.
%H A270837 Giovanni Resta, <a href="/A270837/b270837.txt">Table of n, a(n) for n = 1..47</a> (terms < 10^13)
%e A270837 17 is a term because sigma(16)+phi(16) = 31+8 = 39 = (5*17-7)/2.
%t A270837 Select[Range[10^6], DivisorSigma[1, # - 1] + EulerPhi[# - 1] == (5 # - 7)/2 &] (* _Michael De Vlieger_, Mar 24 2016 *)
%o A270837 (Magma) [n: n in[2..10^7] | 2*(SumOfDivisors(n-1) + EulerPhi(n-1)) eq 5*n-7];
%o A270837 (PARI) lista(nn) = {for(n=2, nn, if(sigma(n-1) + eulerphi(n-1) == (5*n-7)/2, print1(n, ", "))); } \\ _Altug Alkan_, Mar 23 2016
%Y A270837 Cf. A000010, A000051, A000203, A065387, A270779, A270836.
%K A270837 nonn
%O A270837 1,1
%A A270837 _Jaroslav Krizek_, Mar 23 2016
%E A270837 a(29)-a(31) from _Michel Marcus_, Apr 05 2016
%E A270837 a(32)-a(35) from _Giovanni Resta_, Apr 11 2016