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.

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

Author

Amiram Eldar, Apr 29 2023

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

The infinitary version of A057635.

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

Programs

Mathematica

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

Formula

a(A362486(n)) = 0.