A228015 Smallest integer m > n such that phi(m+n) = sigma(m-n).

4, 7, 22, 11, 16, 29, 26, 31, 56, 16, 17, 27, 56, 24, 21, 49, 62, 24, 33, 71, 35, 32, 35, 51, 94, 48, 49, 42, 43, 56, 86, 46, 53, 121, 49, 62, 176, 52, 59, 95, 106, 80, 65, 72, 332, 68, 214, 111, 73, 74, 97, 74, 99, 111, 232, 181, 470, 88, 89, 275, 91, 2019, 132, 98, 89, 128, 212, 114, 156, 257

Offset

1,1

Comments

It seems that for all n, a(n)/n <= 2019/62. [Farideh Firoozbakht, Aug 22 2014]

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Example

For n=1 and m = 2 and 3 phi(m+1) != sigma(m-1), but for m=4 phi(m+1) = sigma(m-1). Thus a(1) = 4.

Maple

with(numtheory):
a:= proc(n) local m;
      for m from n+1 while phi(m+n)<>sigma(m-n) do od; m
    end:
seq(a(n), n=1..80);  # Alois P. Heinz, Aug 05 2013

Mathematica

a[m_]:=(For[n=m+1, DivisorSigma[1, n-m]!=EulerPhi[n+m], n++]; n); Table[a[n], {n, 70}]

Crossrefs

Sequence in context: A186335 A010363 A119561 * A145931 A026548 A100098

Adjacent sequences: A228012 A228013 A228014 * A228016 A228017 A228018

Keyword

nonn

Author

Farideh Firoozbakht, Aug 02 2013

Status

approved