A071939 a(n) = Max { sigma(k) : k = 1, 2, 3, ..., n } - Max { Phi(k) : k = 1, 2, 3, ..., n }.

0, 2, 2, 5, 3, 8, 6, 9, 9, 12, 8, 18, 16, 16, 16, 19, 15, 23, 21, 24, 24, 24, 20, 38, 38, 38, 38, 38, 32, 44, 42, 42, 42, 42, 42, 61, 55, 55, 55, 55, 51, 56, 54, 54, 54, 54, 50, 78, 78, 78, 78, 78, 72, 72, 72, 72, 72, 72, 66, 110, 108, 108, 108, 108, 108, 108, 102, 102, 102

Offset

1,2

Comments

Is there a simple expression for lim_{n->oo} a(n)/n?

Links

Table of n, a(n) for n=1..69.

Formula

a(n) = A070324(n) - A070320(n).

Mathematica

nn=70; With[{sig=DivisorSigma[1, Range[nn]], phi=EulerPhi[Range[ nn]]}, Table[ Max[Take[sig, n]]-Max[Take[phi, n]], {n, nn}]] (* Harvey P. Dale, May 06 2012 *)

Prog

(PARI) for(n=1, 100, v=vector(n, x, sigma(x)); w=vector(n, y, eulerphi(y)); print1(vecmax(v)-vecmax(w), ", "))

Crossrefs

Sequence in context: A368207 A266981 A045893 * A338332 A075545 A006307

Adjacent sequences: A071936 A071937 A071938 * A071940 A071941 A071942

Keyword

easy,nonn

Author

Benoit Cloitre, Jun 15 2002

Status

approved