A065389 - OEIS

%I #14 Jul 20 2023 12:51:16

%S 1,3,5,7,11,13,17,19,25,29,31,37,43,53,61,73,97,109,127,143,151,157,

%T 181,211,241,313,331,337,397,403,421,527,541,601,631,661,757,779,899,

%U 1009,1147,1201,1321,1333,1517,1621,1763,1801,2017,2161,2341,2501,2521

%N Numbers n such that sigma(phi(n)) sets a new record, i.e., sigma(phi(m)) > sigma(phi(k)) for all k < m numbers.

%H Harry J. Smith, <a href="/A065389/b065389.txt">Table of n, a(n) for n = 1..500</a>

%F Numbers at which A000203(A000010(n)) = A062402(n) reaches a new maximal value.

%e A062402 begins {1, 1, 3, 3, 7, 3, 12, 7, 12, 7, 18, 7, 28, 12, 15, 15, 31, 12, 39, 15, 28, 18, 36, 15, 42}. New peaks are reached at positions 3, 5, 7, 11, 13, 17, 19, 25. These peak values are 3, 7, 12, 18, 28, 31, 39, 42 respectively.

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

%t DeleteDuplicates[Table[{n,DivisorSigma[1,EulerPhi[n]]},{n,2600}],GreaterEqual[#1[[2]],#2[[2]]]&][[;;,1]] (* _Harvey P. Dale_, Jul 20 2023 *)

%o (PARI) { n=r=0; for (m=1, 10^9, x=sigma(eulerphi(m)); if (x > r, r=x; write("b065389.txt", n++, " ", m); if (n==500, return)) ) } \\ _Harry J. Smith_, Oct 18 2009

%Y Cf. A000010, A000203, A062402, A065390-A065294.

%K nonn

%O 1,2

%A _Labos Elemer_, Nov 05 2001