A362667 -id:A362667 - cp's OEIS frontend

A362668 a(n) = A091732(A362667(n)).

1, 2, 3, 4, 6, 8, 12, 16, 18, 20, 24, 36, 48, 60, 64, 72, 80, 90, 96, 108, 120, 128, 132, 144, 192, 240, 288, 360, 384, 432, 480, 528, 576, 648, 672, 720, 792, 864, 960, 1008, 1080, 1104, 1152, 1440, 1728, 1920, 2160, 2304, 2592, 2880, 3072, 3168, 3456, 3600, 3840

Offset: 1

Amiram Eldar, Apr 29 2023

nonn

Amiram Eldar, Table of n, a(n) for n = 1..300

The infinitary version of A036912.
Indices of records of A362666.
Cf. A091732, A362484, A362667.

s[n_] := If[(inv = invIPhi[n]) == {}, 0, Max[inv]]; seq[kmax_] := Module[{v = {}, s1, sm = 0}, Do[s1 = s[k]; If[s1 > sm, sm = s1; AppendTo[v, k]], {k, 1, kmax}]; v]; seq[4000] (* using the function invIPhi from A362484 *)

A362666 a(n) is the largest m such that iphi(m) = n, where iphi is the infinitary totient function A091732, or a(n) = 0 if no such m exists.

Original entry on oeis.org

2, 6, 8, 10, 0, 24, 0, 30, 0, 22, 0, 42, 0, 0, 32, 54, 0, 56, 0, 66, 0, 46, 0, 120, 0, 0, 0, 58, 0, 96, 0, 102, 0, 0, 0, 168, 0, 0, 0, 110, 0, 86, 0, 138, 128, 94, 0, 216, 0, 0, 0, 106, 0, 152, 0, 174, 0, 118, 0, 264, 0, 0, 0, 270, 0, 184, 0, 0, 0, 142, 0, 312

Offset: 1

Amiram Eldar, Apr 29 2023

nonn

			a(1) = 2 since there are two solutions to iphi(x) = 1: 1 and 2, and 2 is the larger of them.
a(6) = 24 since there are four solutions to iphi(x) = 6: 7, 12, 14 and 24, and 24 is the largest of them.

Amiram Eldar, Table of n, a(n) for n = 1..10000

The infinitary version of A057635.

Cf. A091732, A362484, A362486 (positions of 0's), A362667 (record values), A362668 (indices of records).

a[n_] := If[(inv = invIPhi[n]) == {}, 0, Max[inv]]; Array[a, 100] (* using the function invIPhi from A362484 *)

a(A362486(n)) = 0.

cp's OEIS Frontend

A362668 a(n) = A091732(A362667(n)).

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