A270837 Numbers n such that sigma(n-1)+phi(n-1) = (5n-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

1,1

Comments

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

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

Prime terms are in A270779.

Links

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

Example

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A144753 A220221 A212292 * A057482 A114136 A025072

Adjacent sequences: A270834 A270835 A270836 * A270838 A270839 A270840

Keyword

nonn

Author

Jaroslav Krizek, Mar 23 2016

Extensions

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

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

Status

approved