A065385 Numbers m at which value of cototient function (A051953) reaches a new record: cototient(m) > cototient(k) for all k < m.

1, 2, 4, 6, 10, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 102, 108, 114, 120, 126, 132, 138, 144, 150, 168, 180, 198, 204, 210, 240, 252, 264, 270, 294, 300, 330, 360, 378, 390, 420, 450, 462, 480, 504, 510, 540, 546, 570, 600, 630, 660, 690, 714

Offset

1,2

Comments

For totient values prime numbers give similar records.

Links

Harry J. Smith, Table of n, a(n) for n = 1..1000

Formula

a=0; s=0; Do[s=n-EulerPhi[n]; If[s>a, a=s; Print[n]], {n, 1, 10000}]

Example

a(8) = 30 because for m = 1...29 the cototient values are all smaller than cototient(30) = 22 = A065386(8) and this is the 8th number at which such a record is reached; analogous sequences are A002093, A002182, A015702 or A005250 for functions other than cototient.

Mathematica

With[{s = Array[# - EulerPhi@ # &, 10^3]}, Map[FirstPosition[s, #][[1]] &, Union@ FoldList[Max, s]]] (* Michael De Vlieger, May 16 2018 *)

Prog

(PARI) r=-1; for(n=1, 1000, d=n-eulerphi(n); if(r<d, r=d; print1(n, ", ")))
(PARI) { n=0; x=-1; for (m=1, 10^9, c=m - eulerphi(m); if (c > x, x=c; write("b065385.txt", n++, " ", m); if (n==1000, return)) ) } \\ Harry J. Smith, Oct 17 2009

Crossrefs

Cf. A051953, A065386.

Sequence in context: A045958 A076067 A316460 * A244052 A324059 A055235

Adjacent sequences: A065382 A065383 A065384 * A065386 A065387 A065388

Keyword

nonn

Author

Labos Elemer, Nov 05 2001

Status

approved