A065391 Numbers m such that A062401(m) = phi(sigma(m)) is increasing to a record value, i.e., A062401(m) represents a new peak, so that A062401(m) > A062401(k) for all k < m.

1, 2, 4, 8, 9, 16, 32, 36, 64, 100, 144, 256, 324, 400, 576, 900, 1296, 1600, 2304, 2916, 3600, 5184, 8100, 9216, 11664, 14400, 20736, 22500, 25600, 30276, 32400, 41616, 46656, 57600, 69696, 72900, 82944, 90000, 104976, 115600, 121104, 129600

Offset: 1

Author

Labos Elemer, Nov 05 2001

Keywords

• nonn

Comments

The terms > 2 are exact powers and except for 2, 8 and 32 all the terms seem to be squares.

Indices of records in A062401. - Michael De Vlieger, Dec 06 2018

Examples

			Initial segment of A062401: {1, 2, 2, 6, 2, 4, 4, 8, 12, 6, 4, 12, 6, 8, 8, 30, 6, ...}. The peak values (those exceeding all previous ones) are 1, 2, 6, 8, 12, 30, reached at positions 1, 2, 4, 8, 9, 16, respectively.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..249 (terms below 10^11; terms 1..100 from Harry J. Smith)

Crossrefs

Cf. A000010, A000203, A062401, A062402, A065392.

Programs

Mathematica

a = 0; s = 0; Do[s = EulerPhi[DivisorSigma[1, n]]; If[s > a, a = s; Print[n]], {n, 1, 10^6}]
(* Second program: *)
With[{s = Array[EulerPhi@ DivisorSigma[1, #] &, 2*10^5]}, Map[FirstPosition[s, #][[1]] &, Union@ FoldList[Max, s]]] (* Michael De Vlieger, Dec 06 2018 *)
DeleteDuplicates[Table[{n,EulerPhi[DivisorSigma[1,n]]},{n,150000}],GreaterEqual[ #1[[2]],#2[[2]]]&] [[;;,1]] (* Harvey P. Dale, May 12 2023 *)

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