A065389 Numbers n such that sigma(phi(n)) sets a new record, i.e., sigma(phi(m)) > sigma(phi(k)) for all k < m numbers.

1, 3, 5, 7, 11, 13, 17, 19, 25, 29, 31, 37, 43, 53, 61, 73, 97, 109, 127, 143, 151, 157, 181, 211, 241, 313, 331, 337, 397, 403, 421, 527, 541, 601, 631, 661, 757, 779, 899, 1009, 1147, 1201, 1321, 1333, 1517, 1621, 1763, 1801, 2017, 2161, 2341, 2501, 2521

Offset

1,2

Links

Harry J. Smith, Table of n, a(n) for n = 1..500

Formula

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

Example

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.

Mathematica

a=0; s=0; Do[s=DivisorSigma[1, EulerPhi[n]]; If[s>a, a=s; Print[n]], {n, 1, 10000}];
DeleteDuplicates[Table[{n, DivisorSigma[1, EulerPhi[n]]}, {n, 2600}], GreaterEqual[#1[[2]], #2[[2]]]&][[;; , 1]] (* Harvey P. Dale, Jul 20 2023 *)

Prog

(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

Crossrefs

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

Sequence in context: A131261 A100276 A225669 * A123567 A059645 A090190

Adjacent sequences: A065386 A065387 A065388 * A065390 A065391 A065392

Keyword

nonn

Author

Labos Elemer, Nov 05 2001

Status

approved