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

1,2

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

Links

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

Example

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.

Mathematica

a = 0; s = 0; Do[s = EulerPhi[DivisorSigma[1, n]]; If[s > a, a = s; Print[n]], {n, 1, 10^6}]
(* Alternative: *)
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 *)

Prog

(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

Crossrefs

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

Sequence in context: A380733 A331992 A113570 * A161792 A111261 A276773

Adjacent sequences: A065388 A065389 A065390 * A065392 A065393 A065394

Keyword

nonn

Author

Labos Elemer, Nov 05 2001

Status

approved