A361922 Infinitary phi-practical numbers: numbers m such that each k <= m is a subsum of a the multiset {iphi(d) : d infinitary divisor of m}, where iphi is an infinitary analog of Euler's phi function (A091732).

1, 2, 3, 6, 8, 12, 15, 24, 30, 40, 42, 56, 60, 72, 84, 105, 108, 120, 132, 135, 156, 165, 168, 195, 210, 216, 240, 255, 264, 270, 280, 312, 330, 360, 378, 384, 390, 408, 420, 440, 456, 462, 480, 504, 510, 520, 540, 546, 552, 570, 600, 616, 640, 660, 672, 680, 690

Offset: 1

Author

Amiram Eldar, Mar 30 2023

Keywords

• nonn

Links

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

Crossrefs

Cf. A077609, A091732.

Similar sequences: A260653, A286906, A334901.

Programs

Mathematica

f[p_, e_] := p^(2^(-1 + Position[Reverse@IntegerDigits[e, 2], 1]));
iphi[1] = 1; iphi[n_] := Times @@ (Flatten@ (f @@@ FactorInteger[n]) - 1);
idivs[n_] := Sort@ Flatten@ Outer[Times, Sequence @@ (FactorInteger[n] /. {p_, m_Integer} :> p^Select[Range[0, m], BitOr[m, #] == m &])]; idivs[1] = {1};
iPhiPracticalQ[n_] := Module[{s = Sort@ Map[iphi, idivs[n]], ans = True}, Do[If[s[[j]] > Sum[s[[i]], {i, 1, j - 1}] + 1, ans = False; Break[]], {j, 1, Length[s]}]; ans]; Select[Range[700], iPhiPracticalQ]