cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A065392 a(n) = A062401(A065391(n)): phi(sigma(m)) peak values for numbers m (listed in A065391) at which those peaks are first reached.

Original entry on oeis.org

1, 2, 6, 8, 12, 30, 36, 72, 126, 180, 360, 432, 660, 930, 1512, 2160, 3300, 3780, 5184, 6552, 11160, 13860, 19800, 23232, 32760, 45360, 47520, 50400, 58080, 61776, 102300, 110160, 137592, 155520, 163296, 196560, 212960, 252000, 272160, 284580
Offset: 1

Views

Author

Labos Elemer, Nov 14 2001

Keywords

Crossrefs

Programs

  • Mathematica
    With[{s = Array[EulerPhi@ DivisorSigma[1, #] &, 10^5]}, Union@ FoldList[Max, s] ] (* Michael De Vlieger, Dec 06 2018 *)
  • PARI
    { n=r=0; for (m=1, 10^9, x=eulerphi(sigma(m)); if (x > r, r=x; write("b065392.txt", n++, " ", x); if (n==100, return)) ) } \\ Harry J. Smith, Oct 18 2009

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

Original entry on oeis.org

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

Views

Author

Labos Elemer, Nov 05 2001

Keywords

Comments

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

Examples

			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.
		

Crossrefs

Programs

  • 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 *)
  • 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

A065390 Peak values reached by A062402 at the sites listed in A065389.

Original entry on oeis.org

1, 3, 7, 12, 18, 28, 31, 39, 42, 56, 72, 91, 96, 98, 168, 195, 252, 280, 312, 360, 372, 392, 546, 576, 744, 840, 864, 992, 1092, 1170, 1344, 1512, 1680, 1860, 1872, 2016, 2240, 2418, 2880, 3224, 3600, 3844, 4320, 4368, 4914, 5082, 5952, 6045, 6552, 7440
Offset: 1

Views

Author

Labos Elemer, Nov 05 2001

Keywords

Crossrefs

Programs

  • Mathematica
    a=0; s=0; Do[s=DivisorSigma[1, EulerPhi[n]]; If[s>a, a=s; Print[s]], {n, 1, 10000}]
    (* Second program: *)
    Union@ FoldList[Max, Array[DivisorSigma[1, EulerPhi[#]] &, 2200]] (* Michael De Vlieger, Jun 19 2018 *)
  • PARI
    { n=r=0; for (m=1, 10^9, x=sigma(eulerphi(m)); if (x > r, r=x; write("b065390.txt", n++, " ", x); if (n==500, return)) ) } \\ Harry J. Smith, Oct 18 2009

Formula

a(n) = A062402(A065389(n)). - Amiram Eldar, Mar 22 2025
Showing 1-3 of 3 results.