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%I #20 May 12 2023 19:28:03
%S 1,2,4,8,9,16,32,36,64,100,144,256,324,400,576,900,1296,1600,2304,
%T 2916,3600,5184,8100,9216,11664,14400,20736,22500,25600,30276,32400,
%U 41616,46656,57600,69696,72900,82944,90000,104976,115600,121104,129600
%N Numbers n such that A062401(n) = phi(sigma(n)) is increasing; i.e., A062401(n) represents a new peak, so that A062401(n) > A062401(k) for all k < n.
%C Indices of records in A062401. - _Michael De Vlieger_, Dec 06 2018
%H Harry J. Smith, <a href="/A065391/b065391.txt">Table of n, a(n) for n = 1..100</a>
%e Initial segment of A062401: {1,2,2,6,2,4,4,8,12,6,4,12,6,8,8,30,6,...}. Peak values [those exceeding all previous ones] are 1,2,6,8,12,30 reached at positions 1,2,4,8,9,16, respectively. Entries > 2 are exact powers and except 2, 8 and 32 seem to be squares.
%t a = 0; s = 0; Do[s = EulerPhi[DivisorSigma[1, n]]; If[s > a, a = s; Print[n]], {n, 1, 10^6}]
%t (* Second program: *)
%t With[{s = Array[EulerPhi@ DivisorSigma[1, #] &, 2*10^5]}, Map[FirstPosition[s, #][[1]] &, Union@ FoldList[Max, s]]] (* _Michael De Vlieger_, Dec 06 2018 *)
%t DeleteDuplicates[Table[{n,EulerPhi[DivisorSigma[1,n]]},{n,150000}],GreaterEqual[ #1[[2]],#2[[2]]]&] [[;;,1]] (* _Harvey P. Dale_, May 12 2023 *)
%o (PARI) { n=r=0; for (m=1, 10^9, x=eulerphi(sigma(m)); if (x > r, r=x; write("b065391.txt", n++, " ", m); if (n==100, return)) ) } \\ _Harry J. Smith_, Oct 18 2009
%Y Cf. A000010, A000203, A062401, A062402, A065392.
%K nonn
%O 1,2
%A _Labos Elemer_, Nov 05 2001
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