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Successive record values of the cototient function (A051953).
3

%I #16 Nov 06 2017 02:51:57

%S 0,1,2,4,6,8,12,16,22,24,30,32,36,44,46,48,54,60,66,70,72,78,88,90,92,

%T 94,96,110,120,132,138,140,162,176,180,184,198,210,220,250,264,270,

%U 294,324,330,342,352,360,382,396,402,426,440,486,500,514,522,528,550,588

%N Successive record values of the cototient function (A051953).

%H Harry J. Smith, <a href="/A065386/b065386.txt">Table of n, a(n) for n = 1..1000</a>

%e a(8)=22 because for m = 1...29 the cototient values are all smaller than cototient(30)=22, where 30=A065385(8) and 22 is the 8th term in the sequence of such local records.

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

%t (* Second program: *)

%t With[{s = Array[# - EulerPhi@ # &, 10^3]}, Union@ FoldList[Max, s]] (* _Michael De Vlieger_, Nov 03 2017 *)

%o (PARI) r=-1; for(n=1,1000,d=n-eulerphi(n); if(r<d,r=d; print1(r,",")))

%o (PARI) { n=0; x=-1; for (m=1, 10^9, c=m - eulerphi(m); if (c > x, x=c; write("b065386.txt", n++, " ", c); if (n==1000, return)) ) } \\ _Harry J. Smith_, Oct 17 2009

%Y Cototient(A065385(n)).

%Y A006093 gives similar records for the totient function. A002093, A002182, A015702, A005250 are analogous sequences for other functions.

%Y a(n) = A051953(A065385(n)).

%Y Cf. A051953, A065386, A000010.

%K nonn

%O 1,3

%A _Labos Elemer_, Nov 05 2001