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

3, 5, 7, 9, 17, 33, 65, 67, 129, 257, 513, 1025, 2049, 4097, 8193, 16385, 32769, 65537, 131073, 262145, 524289, 1048577, 2097153, 4194305, 8388609, 16777217, 33554433, 67108865, 134217729, 268435457, 536870913, 1073741825, 2147483649, 4294967297, 5606129563

Offset: 1

Author

Jaroslav Krizek, Mar 23 2016

Keywords

• nonn

Comments

Numbers k such that A065387(k-1) = (5*k-7)/2.

Numbers of the form 2^k + 1 for k >= 1 from A000051 are terms.

Prime terms are in A270779.

Examples

			17 is a term because sigma(16)+phi(16) = 31+8 = 39 = (5*17-7)/2.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..47 (terms < 10^13)

Crossrefs

Cf. A000010, A000051, A000203, A065387, A270779, A270836.

Programs

Magma

[n: n in[2..10^7] | 2*(SumOfDivisors(n-1) + EulerPhi(n-1)) eq 5*n-7];

Mathematica

Select[Range[10^6], DivisorSigma[1, # - 1] + EulerPhi[# - 1] == (5 # - 7)/2 &] (* Michael De Vlieger, Mar 24 2016 *)

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

Extensions

a(29)-a(31) from Michel Marcus, Apr 05 2016

a(32)-a(35) from Giovanni Resta, Apr 11 2016