A362487 -id:A362487 - cp's OEIS frontend

A362488 Record values in A362487.

2, 4, 6, 10, 14, 18, 22, 30, 34, 40, 48, 58, 60, 92, 136, 146, 184, 232, 240, 342, 478, 518, 638, 772, 830, 924, 1080, 1264, 1330, 1340, 1462, 1824, 2132, 2528, 2710, 3224, 3354, 4084, 4672, 4812, 4976, 5912, 6496, 7606, 8230, 8698, 11472, 12354, 16580, 19250

Offset: 1

Amiram Eldar, Apr 22 2023

nonn

Cf. A362484, A362487.

Similar sequences: A101373, A131934, A361971, A362184.

solnum[n_] := Length[invIPhi[n]]; seq[kmax_] := Module[{s = {}, solmax=0}, Do[sol = solnum[k]; If[sol > solmax, solmax = sol; AppendTo[s, sol]], {k, 1, kmax}]; s]; seq[10^4] (* using the function invIPhi from A362484 *)

a(n) = A362485(A362487(n)).

A362485 Number of numbers k such that iphi(k) = n, where iphi is the infinitary totient function A091732.

Original entry on oeis.org

2, 2, 2, 2, 0, 4, 0, 4, 0, 2, 0, 6, 0, 0, 2, 4, 0, 4, 0, 2, 0, 2, 0, 10, 0, 0, 0, 2, 0, 6, 0, 4, 0, 0, 0, 8, 0, 0, 0, 4, 0, 2, 0, 2, 2, 2, 0, 14, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, 10, 0, 0, 0, 4, 0, 4, 0, 0, 0, 2, 0, 14, 0, 0, 0, 0, 0, 2, 0, 8, 0, 2, 0, 4, 0, 0

Offset: 1

Amiram Eldar, Apr 22 2023

nonn

a(n) is even for all n, because if k is a solution to iphi(k) = n, and A007814(k) is even, then 2*k is also a solution, i.e., iphi(2*k) = n.

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

Row lengths of A362484.
Cf. A007814, A091732, A362486 (positions of 0's), A362487 (indices of records).
Similar sequences: A014197, A063740, A361967, A362181.

a[n_] := Length[invIPhi[n]]; Array[a, 100] (* using the function invIPhi from A362484 *)

a(A362486(n)) = 0.

cp's OEIS Frontend

A362488 Record values in A362487.

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