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
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With[{s = Array[EulerPhi@ DivisorSigma[1, #] &, 10^5]}, Union@ FoldList[Max, s] ] (* Michael De Vlieger, Dec 06 2018 *)
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{ 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
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.
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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 *)
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{ 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
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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 *)
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{ 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
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