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

3, 5, 9, 11, 17, 33, 65, 129, 231, 257, 513, 1025, 2049, 4097, 8193, 16385, 32769, 65537, 119831, 131073, 262145, 524289, 1048577, 2097153, 4194305, 8388609, 16777217, 33554433, 67108865, 134217729, 268435457, 536870913, 1073741825, 2147483649, 4294967297

Offset

1,1

Comments

Numbers n such that A051612(n-1) = (3n-5)/2.

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

Prime terms are in A270778.

Links

Giovanni Resta, Table of n, a(n) for n = 1..46 (terms < 10^13)

Example

17 is a term because sigma(16) - phi(16) = 31-8 = 23 = (3*17-5)/2.

Mathematica

Select[Range[10^6], 2 (DivisorSigma[1, # - 1] - EulerPhi[# - 1]) == 3 # - 5 &] (* Michael De Vlieger, Mar 24 2016 *)

Prog

(Magma) [n: n in[1..10^7] | 2*(SumOfDivisors(n-1) - EulerPhi(n-1)) eq 3*n-5]
(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

Crossrefs

Cf. A000010, A000051, A000203, A051612, A270778, A270837.

Sequence in context: A340287 A123069 A356537 * A100456 A059819 A074986

Adjacent sequences: A270833 A270834 A270835 * A270837 A270838 A270839

Keyword

nonn

Author

Jaroslav Krizek, Mar 23 2016

Extensions

a(30)-a(32) from Michel Marcus, Apr 05 2016

a(33)-a(35) from Giovanni Resta, Apr 11 2016

Status

approved